Executive Employment Agreement - NUMAR Corp., Halliburton Co. and Melvin N. Miller


                        EXECUTIVE EMPLOYMENT AGREEMENT


     This Executive Employment Agreement ('Agreement'), including the attached
Exhibit 'A', is entered into by and between NUMAR Corporation, a Pennsylvania
corporation having offices at 508 Lapp Road, Malvern, Pennsylvania 19355
('Employer'), Halliburton Company, a Delaware corporation having offices at 3600
Lincoln Plaza, 500 N. Akard Street, Dallas, Texas 75201-3391 ('Halliburton'),
and Melvin N. Miller, an individual currently residing at 475 Warick Road,
Wynnewood, PA 19096 ('Employee'), to be effective at the effective date that
Employer becomes a subsidiary of Halliburton (the 'Effective Date').

                             W I T N E S S E T H:

     WHEREAS, Halliburton Company has proposed to acquire Employer as a
subsidiary of Halliburton; and

     WHEREAS, Employee is currently employed by Employer; and

     WHEREAS, Employer is desirous of continuing the employment of Employee
after the effective date that Employer becomes a subsidiary of Halliburton
pursuant to the terms and conditions and for the consideration set forth in this
Agreement, and Employee is desirous of continuing in the employ of Employer
pursuant to such terms and conditions and for such consideration.

     NOW, THEREFORE, for and in consideration of the mutual promises, covenants,
and obligations contained herein, Employer and Employee agree as follows:

ARTICLE I: EMPLOYMENT AND DUTIES:

     1.1.  Employer agrees to employ Employee, and Employee agrees to be
employed by Employer, beginning as of the Effective Date and continuing until
December 31, 2001 (the 'Term'), subject to the terms and conditions of this
Agreement.

     1.2.  Beginning as of the Effective Date, Employee shall be employed as
President of Employer. Employee agrees to serve in the assigned position and to
perform diligently and to the best of Employee's abilities the duties and
services appertaining to such position as reasonably determined by Employer, as
well as such additional or different duties and services appropriate to such
position which Employee from time to time may be reasonably directed to perform
by Employer. Employee shall at all times comply with and be subject to such
policies and procedures as Employer or Halliburton may establish from time to
time, including, without limitation, Halliburton's Code of Business Conduct.

 
     During the Term, Employee shall report to the Board of Directors of
Employer. In addition, Employee shall report to a senior executive of
Halliburton designated by Halliburton from time to time. Directions from such
senior executive of Halliburton shall be considered as directions from Employer
for purposes of this Agreement.

     1.3.  Employee shall, during the period of Employee's employment by
Employer, devote Employee's full business time, energy, and best efforts to the
business and affairs of Employer. Employee may not engage, directly or
indirectly, in any other business, investment, or activity that interferes with
Employee's performance of Employee's duties hereunder, is contrary to the
interest of Employer or its affiliates, or requires any significant portion of
Employee's business time. The foregoing notwithstanding, the parties recognize
and agree that Employee may engage in passive personal investments and other
business activities which do not conflict with the business and affairs of the
Employer or its affiliates or interfere with Employee's performance of his
duties hereunder. Employee may not serve on the board of directors of any entity
other than the Employer during the Term without the approval of the Audit
Committee of Halliburton's Board of Directors in accordance with Halliburton's
policies and procedures regarding such service, which approval will not be
unreasonably withheld. Employee shall be permitted to retain any compensation
received for service on any unaffiliated corporation's board of directors.

     1.4.  Employee acknowledges and agrees that Employee owes a fiduciary duty
of loyalty, fidelity and allegiance to act at all times in the best interest of
the Employer to do no act which would intentionally injure Employer's business,
its interests, or its reputation. It is agreed that any direct or indirect
interest in, connection with, or benefit from any outside activities,
particularly commercial activities, which interest might in any way adversely
affect Employer, or any of its affiliates, involves a possible conflict of
interest. In keeping with Employee's fiduciary duties to Employer, Employee
agrees that Employee shall not knowingly become involved in a conflict of
interest with Employer or its affiliates, or upon discovery thereof, allow such
a conflict to continue. Moreover, Employee agrees that Employee shall disclose
to the Audit Committee of Halliburton's Board of Directors any facts which might
involve a possible conflict of interest.

ARTICLE 2: COMPENSATION AND BENEFITS:

     2.1.  Employee's base salary during the Term shall be not less than
$250,000 per annum which shall be paid in accordance with the Employer's
standard payroll practice for its executives.

     2.2.  Beginning January 1, 1998 and continuing for the remainder of the
Term, Employee shall participate in an incentive compensation plan adopted by
the Board of Directors of Employer for senior executives of Employer, subject to
approval of such plan in accordance with Halliburton's policies and procedures
as in effect from time to time. Such

                                       2

 
plan shall provide that Employee shall have an opportunity to earn an annual
incentive bonus of up to 70% of his base salary if the objectives of such plan,
as established by the Board of Directors of Employer in its complete discretion
on an annual basis, are achieved in full. The foregoing notwithstanding, nothing
herein shall prevent or prohibit Employer from modifying such incentive
compensation plan or replacing such plan with a substitute incentive
compensation plan as provided in Section 2.8 hereof.

     2.3.  As of the Effective Date and in consideration of the promises
contained herein, Halliburton shall grant to Employee under the Halliburton
Company 1993 Stock and Long-Term Incentive Plan a nonqualified stock option to
purchase 12,500 shares of Halliburton's common stock. The form and other terms
and conditions of such option (other than the exercise price, which shall be the
closing price of Halliburton's common stock on the New York Stock Exchange on
the Effective Date) are set forth in Exhibit A attached to, and forming a part
of, this Agreement.

     2.4.  As of the Effective Date, Employee shall continue to be entitled to
all his rights under outstanding stock options held by Employee prior to the
Effective Date, and nothing herein shall or is intended to affect any of such
rights.

     2.5.  Beginning January 1, 1998 and continuing for the remainder of the
Term while Employee is employed by Employer hereunder, Employee will be
designated as a participant in the Halliburton Company Senior Executives'
Deferred Compensation Plan. For the years 1998, 1999, 2000 and 2001, Employee
will receive an allocation of at least $62,500 to his Deferred Compensation
Account thereunder at the end of each full calendar year provided he was
employed by Employer throughout the calendar year for which such allocation is
to be made.

     2.6.  From and after the Effective Date, Employer shall pay, or reimburse
Employee, for all ordinary, reasonable and necessary expenses which Employee
incurs in performing his duties under this Agreement including, but not limited
to, travel, entertainment, professional dues and subscriptions, and all dues,
fees and expenses associated with membership in various professional, business
and civic associations and societies of which Employee's participation is in the
best interest of Employer.

     2.7.  While employed by Employer, Employee shall be allowed to participate,
on the same basis generally as other employees of Employer, in all general
employee benefit plans and programs, including improvements or modifications of
the same, which on the Effective Date or thereafter are made available by
Employer to all or substantially all of Employer's executive employees. Such
benefits, plans, and programs may include, without limitation, medical, health,
and dental care, life insurance, disability protection, and qualified retirement
plans but, except as otherwise provided in Section 2.2 and in the last sentence
of this Section 2.7, shall not include any incentive compensation or bonus plans
or programs. Except as specifically provided herein, nothing in this Agreement
is to be construed or

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interpreted to provide greater rights, participation, coverage, or benefits
under such benefit plans or programs than provided to executive employees
pursuant to the terms and conditions of such benefit plans and programs. While
employed by Employer, Employee shall be eligible to receive grants of stock
options under the Halliburton Company 1993 Stock and Long-Term Incentive Plan
and any other stock option plans adopted by Halliburton.

     2.8.  Neither Employer nor Halliburton shall by reason of this Article 2 be
obligated to institute, maintain, or refrain from changing, amending, or
discontinuing, any incentive compensation or employee benefit program or plan,
so long as such actions are similarly applicable to covered employees generally.

     2.9.  Employer may withhold from any compensation, benefits, or amounts
payable under this Agreement all federal, state, city, or other taxes as may be
required pursuant to any law or governmental regulation or ruling.

ARTICLE 3: TERMINATION PRIOR TO EXPIRATION OF TERM AND EFFECTS OF SUCH
           TERMINATION:

     3.1.  Employee's employment with Employer shall be terminated (i) upon the
death of Employee, (ii) upon Employee's permanent disability (permanent
disability being defined as Employee's physical or mental incapacity to perform
his usual duties as an employee with such condition likely to remain
continuously and permanently), or (iii) at any time during the Term by Employer
upon notice to Employee or by Employee upon 60 days' notice to Employer for any
or no reason; provided, however, that Employer shall not terminate Employee's
employment for any reason, except for 'Cause' (as hereinafter defined), prior to
six (6) months following the Effective Date.

     3.2.  If Employee's employment is terminated by reason of a 'Voluntary
Termination' (as hereinafter defined), the death of Employee, permanent
disability of Employee (as defined in Section 3.1) or by the Employer for Cause,
all future compensation to which Employee is otherwise entitled and all future
benefits for which Employee is eligible shall cease and terminate as of the date
of termination, except as specifically provided in this Section 3.2. Benefits
payable to Employee pursuant to the plans, programs or stock option agreements
specified or referred to in Sections 2.2, 2.3, 2.4 or 2.5 shall be made in
accordance with such plans, programs, stock option agreements and the provisions
of such Sections. Employee, or his estate in the case of Employee's death, shall
be entitled to pro rata base salary through the date of such termination and
shall be entitled to any individual bonuses or individual incentive compensation
not yet paid but due under Employer's plans but shall not be entitled to any
other payments by or on behalf of Employer except for those which may be payable
pursuant to the terms of Employer's employee benefit plans (as hereinafter
defined).  For purposes of this Section 3.2, a 'Voluntary Termination' of the
employment relationship by Employee prior to expiration of the Term shall be a

                                       4

 
termination of employment in the sole discretion of and at the election of
Employee, other than (i) a termination of Employee's employment because of a
material breach by Employer of any material provision of this Agreement which
remains uncorrected for thirty (30) days following written notice of such breach
by Employee to Employer or (ii) a termination of Employee's employment within
six (6) months of a change in Employee's title to a less senior position,
material reduction in his responsibility with Employer or requirement for
Employee to be based at a location outside a 60-mile radius of Malvern,
Pennsylvania. For purposes of this Section 3.2, the term 'Cause' shall mean any
of (i) Employee's willful misconduct in the performance of the duties and
services required of Employee pursuant to this Agreement that has a material
adverse effect on Employer; (ii) Employee's final conviction of a felony; (iii)
Employee's material breach of any material provision of this Agreement which
remains uncorrected for thirty (30) days following written notice to Employee by
Employer of such breach which specifies the basis for the breach in detail; (iv)
a material violation of Halliburton's Code of Business Conduct; or (v)
Employee's breach of the Affiliate's Agreement between Employee and Halliburton
dated June __, 1997. No act or failure shall be deemed 'willful' if due
primarily to an error in judgment or negligence or if in good faith and with
reasonable belief that such act is in the best interest of Employer.

     3.3.  If Employee's employment is terminated for any reason other than as
described in Section 3.2 above during the Term, (i) all of Employee's
outstanding options to purchase shares of Halliburton common stock granted
pursuant to Section 2.3 hereof shall vest and become immediately exercisable,
and (ii) Employer shall continue to pay to Employee as a severance benefit his
base salary at the rate in effect on the date of Employee's termination of
employment for the remainder of the unexpired Term; provided, however, that the
aggregate amount of such payments shall not be less than $250,000.  The
severance benefit paid pursuant to this Section 3.3 to Employee shall be in
consideration of Employee's continuing obligations hereunder after such
termination (including, without limitation, Employee's non-competition
obligations). Employee shall not be under any duty or obligation to seek or
accept other employment following a termination of employment pursuant to which
severance benefit payments under this Section 3.3 are owing and the amounts due
Employee pursuant to this Section 3.3 shall not be reduced or suspended if
Employee accepts subsequent employment or earns any amounts as a self-employed
individual.

     Employee's rights under this Section 3.3 are Employee's sole and exclusive
rights against the Employer or its affiliates and the Employer's sole and
exclusive liability to Employee under this Agreement, in contract, tort or
otherwise, for the termination of his employment relationship with Employer.
Employee covenants not to sue or lodge any claim, demand or cause of action
against Employer based upon Employee's termination of employment for any monies
other than those specified in this Section 3.3 and except for any claims
Employee may have for benefits under the plans, programs and stock options
specified or referred to in Sections 2.2, 2.3, 2.4 or 2.5.  If Employee breaches
this covenant, Employer shall be entitled to recover from Employee all sums
expended by Employer

                                       5

 
(including costs and attorneys' fees), in connection with such suit, claim,
demand or cause of action. Nothing contained in this Section 3.3 shall be
construed to be a waiver by Employee of any benefits accrued for or due Employee
under any employee benefit plan (as such term is defined in the Employees'
Retirement Income Security Act of 1974, as amended) maintained by Employer,
except that Employee shall not be entitled to any severance benefits pursuant to
any severance plan or program of the Employer or Halliburton.

     3.4.  Termination of the employment relationship does not terminate those
obligations imposed by this Agreement which are continuing obligations,
including, without limitation, Employee's obligations under Articles 4 and 5.

ARTICLE 4: OWNERSHIP AND PROTECTION OF INTELLECTUAL PROPERTY AND CONFIDENTIAL
           INFORMATION:

     4.1.  All information, ideas, concepts, improvements, discoveries, and
inventions, whether patentable or not, which are conceived, made, developed or
acquired by Employee, individually or in conjunction with others, during
Employee's employment by Employer (whether during business hours or otherwise
and whether on Employer's premises or otherwise) which relate to Employer's
business, products or services (including, without limitation, all such
information relating to corporate opportunities, research, financial and sales
data, pricing and trading terms, evaluations, opinions, interpretations,
acquisition prospects, the identity of customers or their requirements, the
identity of key contacts within the customer's organizations or within the
organization of acquisition prospects, or marketing and merchandising
techniques, prospective names, and marks), and all writings or materials of any
type embodying any of such items, shall be the sole and exclusive property of
Employer.

     4.2.  Employee acknowledges that the businesses of Employer and its
affiliates are highly competitive and that their strategies, methods, books,
records, and documents, their technical information concerning their products,
equipment, services, and processes, procurement procedures and pricing
techniques, the names of and other information (such as credit and financial
data) concerning their customers and business affiliates, all comprise
confidential business information and trade secrets which are valuable, special,
and unique assets which Employer or its affiliates use in their business to
obtain a competitive advantage over their competitors.  Employee further
acknowledges that protection of such confidential business information and trade
secrets against unauthorized disclosure and use is of critical importance to
Employer and its affiliates in maintaining their competitive position. Employee
hereby agrees that Employee will not, at any time during or after his employment
by Employer, make any unauthorized disclosure of any confidential business
information or trade secrets of Employer or its affiliates, or make any use
thereof, except in the carrying out of his employment responsibilities
hereunder. Confidential business information shall not include information in
the public domain (but only if the same becomes part of the public domain
through a means other than a disclosure prohibited hereunder).  The above

                                       6

 
notwithstanding, a disclosure shall not be unauthorized if (i) it is required by
law or by a court of competent jurisdiction or (ii) it is in connection with any
judicial or other legal proceeding in which Employee's legal rights and
obligations as an employee or under this Agreement are at issue; provided,
however, that Employee shall, to the extent practicable and lawful in any such
events, give prior notice to Employer of his intent to disclose any such
confidential business information in such context so as to allow Employer an
opportunity (which Employee will not oppose) to obtain such protective orders or
similar relief with respect thereto as it may deem appropriate.

     4.3.  All written materials, records, and other documents made by, or
coming into the possession of, Employee during the period of Employee's
employment by Employer which contain or disclose confidential business
information or trade secrets of Employer or its affiliates shall be and remain
the property of Employer, or its affiliates, as the case may be. Upon
termination of Employee's employment by Employer, for any reason, Employee
promptly shall deliver the same, and all copies thereof, to Employer.

ARTICLE 5: POST-EMPLOYMENT AND NON-COMPETITION
           OBLIGATIONS:

     5.1.  As part of the consideration for the compensation and benefits to be
paid to Employee hereunder, and as an additional incentive for Employer to enter
into this Agreement, Employer and Employee agree to the non-competition
provisions of this Article 5.  During the term of Employee's employment and for
two (2) years after any termination of employment, or if longer, for so long as
Employee is entitled to the payment of amounts determined in accordance with
Section 3.3 hereof, Employee shall not directly or indirectly:  (i) engage
anywhere in the world, in (a) the manufacture, assembly, design, development,
distribution or marketing of or research with respect to any product, equipment
or service substantially similar to or in competition with any product,
equipment or service which at any time during the term of such employment or the
immediately preceding twelve-month period has been manufactured, sold,
distributed or provided by Employer or any product, equipment or service which
Employer was developing during such period for future manufacture, sale or
distribution or (b) the provision of any service substantially similar to or in
competition with any service offered by Employer at any time during such period;
(ii) be or become a stockholder, partner, owner, officer, director or employee
or agent of, or a consultant to, or give financial or other assistance to, any
person or entity considering engaging in any such activities or so engaged;
(iii) seek in competition with the business of Employer to procure orders from
or do business with any customer of Employer; (iv) solicit, or contact with a
view to the engagement or employment of, any person who is an employee of
Employer; (v) seek to contract with or engage (in such a way as to adversely
affect or interfere with the business of Employer) any person or entity who has
been contracted with or engaged to manufacture, assemble, supply or deliver
products, goods, materials or services to Employer; or (vi) engage in, or
participate in any effort to act to induce any of the customers, associates,
consultants, and employees of Employer or any of its affiliates to take,

                                       7

 
any action which might be disadvantageous to Employer or any of its affiliates;
provided, however, that nothing herein shall prohibit the Employee and his
affiliates from owning, as passive investors, in the aggregate not more than 5%
of the outstanding publicly-traded stock of any corporation so engaged. The
duration of the Employee's covenants set forth in this Section 5.1 shall be
extended by a period of time equal to the number of days, if any, during which
the Employee is in violation of the provisions hereof.

     The term 'Employer' as used in this Section 5.1 shall mean and include (i)
NUMAR Corporation, (ii) NUMAR's subsidiaries and (iii) the wireline logging,
measurement-while-drilling and logging-while-drilling activities (including
research and development) of Halliburton and its affiliates.

     5.2   (A)  Employee acknowledges and agrees that the covenants contained in
Articles 4 and 5 hereof are fair and reasonable in light of the consideration
paid hereunder, and that damages alone shall not be an adequate remedy for any
breach by Employee of his covenants contained herein and accordingly expressly
agrees that:  in addition to any other remedies which Employer may have,
Employer, on its own behalf and on behalf of any of its affiliates, shall be
entitled to injunctive relief in any court of competent jurisdiction for any
breach or threatened breach of any such covenants by Employee.  Nothing
contained herein shall prevent or delay Employer from seeking, in any court of
competent jurisdiction, specific performance or other equitable remedies in the
event of any breach or intended breach by Employee of any of its obligations
hereunder.

           (B)  Notwithstanding the equitable relief available to Employer, the
Employee, in the event of a breach of his covenants contained in Articles 4 and
5 hereof, understands and agrees that the uncertainties and delay inherent in
the legal process would result in the continuing breach for some period of time,
and therefore, continuing injury to Employer until and unless Employer can
obtain such equitable relief.  Therefore, in addition to such equitable relief,
Employer shall be entitled to monetary damages for any such period of breach
until the termination of such breach, in an amount deemed reasonable to cover
all actual and consequential losses, plus all monies received by Employee as a
result of said breach and all costs and attorneys' fees incurred by Employer in
enforcing this Agreement.  If Employee should use or reveal to any other person
or entity any confidential information, this will be considered a continuing
violation on a daily basis for so long a period of time as such confidential
information is made use of by Employee or any such other person or entity.

     5.3.  It is expressly understood and agreed that Employer and Employee
consider the restrictions contained in this Article 5 to be reasonable and
necessary to protect the proprietary information and/or goodwill of Employer.
Nevertheless, if any of the aforesaid restrictions are found by a court having
jurisdiction to be unreasonable or overly broad as to geographic area or time,
or otherwise unenforceable, the parties intend for the restrictions herein set
forth to be modified by such courts so as to be reasonable and enforceable and,
as so modified to be fully enforced.

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ARTICLE 6: MISCELLANEOUS:

     6.1.  For purposes of this Agreement, (i) the terms 'affiliates' or
'affiliated' means an entity who directly, or indirectly through one or more
intermediaries, controls, is controlled by, or is under common control with
Employer, Halliburton or Employee, as the case may be, or in which Employer,
Halliburton or Employee, as the case may be, has a 50% or more equity interest,
and (ii) any action or omission permitted to be taken or omitted by Employer or
Halliburton hereunder shall only be taken or omitted by Employer or Halliburton,
as the case may be, upon the express authority of the Board of Directors of
Employer and/or Halliburton, as applicable, or of any Committee of the
respective Boards to which authority over such matters may have been delegated.

     6.2.  Although executed and delivered by the parties hereto, this Agreement
is contingent upon the Employer becoming a  subsidiary of Halliburton and shall
not become effective until such time as the Employer has become a  subsidiary of
Halliburton.

     6.3.  For purposes of this Agreement, notices and all other communications
provided for herein shall be in writing and shall be deemed to have been duly
given when received by or tendered to Employee, Halliburton or Employer, as
applicable, by pre-paid courier or by United States registered or certified
mail, return receipt requested, postage prepaid, addressed as follows:

     If to Employer or Halliburton, to Halliburton Company at its corporate
     headquarters to the attention of the General Counsel of Halliburton
     Company.

     If to Employee, to his last known personal residence.

     6.4.  This Agreement shall be governed in all respects by the laws of the
Commonwealth of Pennsylvania, without regard to principles of conflict of law,
unless preempted by federal law, in which case federal law shall govern.

     6.5.  No failure by either party hereto at any time to give notice of any
breach by the other party of, or to require compliance with, any condition or
provision of this Agreement shall be deemed a waiver of similar or dissimilar
provisions or conditions at the same or at any prior or subsequent time.

     6.6.  It is a desire and intent of the parties that the terms, provisions,
covenants, and remedies contained in this Agreement shall be enforceable to the
fullest extent permitted by law. If any such term, provision, covenant, or
remedy of this Agreement or the application thereof to any person, association,
or entity or circumstances shall, to any extent, be construed to be invalid or
unenforceable in whole or in part, then such term, provision, covenant, or
remedy shall be construed in a manner so as to permit its enforceability under

                                       9

 
the applicable law to the fullest extent permitted by law. In any case, the
remaining provisions of this Agreement or the application thereof to any person,
association, or entity or circumstances other than those to which they have been
held invalid or unenforceable, shall remain in full force and effect.

     6.7.  This Agreement shall be binding upon and inure to the benefit of
Employer and, to the extent herein provided, Halliburton and any other person,
association, or entity which may hereafter acquire or succeed to all or
substantially all of the business or assets of Employer by any means whether
direct or indirect, by purchase, merger, consolidation, or otherwise. Employee's
rights and obligations under this Agreement are personal and such rights,
benefits, and obligations of Employee shall not be voluntarily or involuntarily
assigned, alienated, or transferred, whether by operation of law or otherwise,
without the prior written consent of Employer, other than in the case of death
or incompetence of Employee.

     6.8.  Effective with the effective date that Employer becomes a subsidiary
of Halliburton, this Agreement shall supersede, replace and merge any previous
actions by Employer's Board of Directors or any Committee of such Board,
agreements and discussions pertaining to the subject matter covered herein,
including, without limitation, the Employment Agreement dated July 18, 1996,
between Employer and Employee.  From and after the Effective Date, this
Agreement constitutes the entire agreement of the parties with regard to such
subject matter, and contains all of the covenants, promises, representations,
warranties, and agreements between the parties with respect such subject matter.
Each party to this Agreement acknowledges that no representation, inducement,
promise, or agreement, oral or written, has been made by either party with
respect to such subject matter, which is not embodied herein, and that no
agreement, statement, or promise relating to the employment of Employee by
Employer that is not contained in this Agreement shall be valid or binding. Any
modification of this Agreement will be effective only if it is in writing and
signed by each party whose rights hereunder are affected thereby, provided that
any such modification must be authorized or approved by the Board of Directors
of Employer.

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     IN WITNESS WHEREOF, Employer, Halliburton and Employee have duly executed
this Agreement in multiple originals to be effective on the Effective Date.

                        NUMAR CORPORATION


                        By: /s/ DR. MELVIN N. MILLER
                            -------------------------------------
                        Name:   Dr. Melvin N. Miller
                        Title:  Chairman of the Board, President
                                and Chief Executive Officer



                        HALLIBURTON COMPANY


                        By: /s/ LESTER L. COLEMAN
                            -------------------------------------
                        Name:   Lester L. Coleman
                        Title:  Executive Vice President and 
                                General Counsel  
                                
                        EMPLOYEE

                            /s/ DR. MELVIN N. MILLER
                            -------------------------------------    
                                Dr.  Melvin N. Miller


Date:  6/9/97

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                                 EXHIBIT A TO
                        EXECUTIVE EMPLOYMENT AGREEMENT
                                BY AND BETWEEN
                      MELVIN N. MILLER, NUMAR CORPORATION
                            AND HALLIBURTON COMPANY



                      NONSTATUTORY STOCK OPTION AGREEMENT

     AGREEMENT made as of the __ day of ____________, 1997 between HALLIBURTON
COMPANY, a Delaware corporation (the 'Company'), and Melvin N. Miller
('Employee').

     To carry out the purposes of the HALLIBURTON COMPANY 1993 STOCK AND LONG-
TERM INCENTIVE PLAN (the 'Plan'), by affording Employee the opportunity to
purchase shares of common stock, par value $2.50 per share, of the Company
('Stock'), and in consideration of the mutual agreements and other matters set
forth herein, in the Executive Employment Agreement by and between NUMAR
Corporation, the Company and Employee and in the Plan, the Company and Employee
hereby agree as follows:

     1.  GRANT OF OPTION.  The Company hereby irrevocably grants to Employee the
         ---------------                                                        
right and option ('Option') to purchase all or any part of an aggregate of
12,500 shares of Stock, on the terms and conditions set forth herein and in the
Plan, which Plan is incorporated herein by reference as a part of this
Agreement. This Option shall not be treated as an incentive stock option within
the meaning of section 422(b) of the Internal Revenue Code of 1986, as amended
(the 'Code').

     2.  PURCHASE PRICE.  The purchase price of Stock purchased pursuant to the
         --------------                                                        
exercise of this Option shall be $________ per share, which has been determined
to be not less than the fair market value of the Stock at the date of grant of
this Option. For all purposes of this Agreement, fair market value of Stock
shall be determined in accordance with the provisions of the Plan.

     3.  EXERCISE OF OPTION.  Subject to the earlier expiration of this Option
         ------------------                                                   
as herein provided, this Option may be exercised, by written notice to the
Company at its principal executive office addressed to the attention of its Vice
President and Secretary, at any time and from time to time after the date of
grant hereof, but, except as otherwise provided below, this Option shall not be
exercisable for more than a percentage of the aggregate number of shares offered
by this Option determined by the number of full years from the date of grant
hereof to the date of such exercise, in accordance with the following schedule:

                                       1

 
 
 
                               Percentage of Shares
     Number of Full Years      That May be Purchased
     --------------------      ---------------------
                             
     Less than 1 year                    0%
     1 year                         33 1/3%
     2 years                            67%
     3 years                           100%
 


     This Option is not transferable by Employee otherwise than by will or the
laws of descent and distribution, and may be exercised only by Employee during
Employee's lifetime. This Option may be exercised only while Employee remains an
employee of the Company, subject to the following exceptions:

          (a)  If Employee's employment with the Company terminates by reason of
     disability (disability being defined as being physically or mentally
     incapable of performing the Employee's usual duties as an Employee with
     such condition likely to remain continuously and permanently, as determined
     by the Company or employing subsidiary), this Option may be exercised in
     full by Employee (or Employee's estate or the person who acquires this
     Option by will or the laws of descent and distribution or otherwise by
     reason of the death of Employee) at any time during the period of one year
     following such termination.

          (b)  If Employee dies while in the employ of the Company, Employee's
     estate, or the person who acquires this Option by will or the laws of
     descent and distribution or otherwise by reason of the death of Employee,
     may exercise this Option in full at any time during the period of one year
     following such termination.

          (c)  If Employee's employment with the Company terminates by reason of
     retirement at or after age 65 or early retirement with consent of the
     Committee administering the Plan or its delegate, as appropriate, this
     Option may be exercised by Employee at any time during the period ending on
     the Expiration Date (as defined below), but only as to the number of shares
     Employee was entitled to purchase on the date of such exercise in
     accordance with the schedule set forth above.  If Employee dies after such
     retirement, this Option may be exercised in full by Employee's estate (or
     the person who acquires this Option by will or the laws of descent and
     distribution or otherwise by reason of the death of Employee) during the
     period ending on the earlier of the Expiration Date or the third
     anniversary of Employee's death.

          (d)  If Employee shall, as a result of the termination of his
     employment with Employer, become entitled to the severance benefits set
     forth in Section 3.3 of that certain Executive Employment Agreement of even
     date herewith by and among Employee, NUMAR Corporation and the Company (the
     'Employment Agreement'), this Option may be exercised in full by Employee
     at any time during 

                                       2

 
     the period of 90 days following such termination or by Employee's estate
     (or the person who acquires this Option by will or the laws of descent and
     distribution or otherwise by reason of the death of the Employee) during
     the period of six months following Employee's death if Employee dies during
     such period. Capitalized terms used in this subparagraph (d) but not
     defined shall have the meanings ascribed in the Employment Agreement. If
     Employee shall become entitled to severance benefits as aforesaid within
     six months from the date of grant of this Option, the time periods
     specified in this subparagraph in which the Option may be exercised shall
     begin at the end of such six month period.

          (e)  If Employee's employment with the Company terminates for any
     reason other than those set forth in subparagraphs (a) through (d) above,
     this Option may be exercised by Employee at any time during the period of
     30 days following such termination, or by Employee's estate (or the person
     who acquires this Option by will or the laws of descent and distribution or
     otherwise by reason of the death of the Employee) during a period of six
     months following Employee's death if Employee dies during such 30-day
     period, but in each case only as to the number of shares Employee was
     entitled to purchase hereunder upon exercise of this Option as of the date
     Employee's employment so terminates.

     This Option shall not be exercisable in any event prior to the expiration
of six months from the date of grant hereof or after the expiration of ten years
from the date of grant hereof (the 'Expiration Date') notwithstanding anything
hereinabove contained. The purchase price of shares as to which this Option is
exercised shall be paid in full at the time of exercise (a) in cash (including
check, bank draft or money order payable to the order of the Company), (b) by
delivering to the Company shares of Stock having a fair market value equal to
the purchase price, or (c) by a combination of cash or Stock. Payment may also
be made, in the discretion of the Committee or its delegate, as appropriate, by
delivery (including by facsimile transmission) to the Company of an executed
irrevocable option exercise form, coupled with irrevocable instructions to a
broker-dealer designated by the Company to simultaneously sell a sufficient
number of the shares as to which the option is exercised and deliver directly to
the Company that portion of the sales proceeds representing the exercise price.
No fraction of a share of Stock shall be issued by the Company upon exercise of
an Option or accepted by the Company in payment of the purchase price thereof;
rather, Employee shall provide a cash payment for such amount as is necessary to
affect the issuance and acceptance of only whole shares of Stock. Unless and
until a certificate or certificates representing such shares shall have been
issued by the Company to Employee, Employee (or the person permitted to exercise
this Option in the event of Employee's death) shall not be or have any of the
rights or privileges of a shareholder of the Company with respect to shares
acquirable upon an exercise of this Option.

     4.   WITHHOLDING OF TAX.  To the extent that the exercise of this Option or
          ------------------                                                    
the disposition of shares of Stock acquired by exercise of this Option results
in compensation income to Employee for federal or state income tax purposes,
Employee shall deliver to the Company at the time of such exercise or
disposition such amount of money or shares of 

                                       3

 
Stock as the Company may require to meet its withholding obligation under
applicable tax laws or regulations, and, if Employee fails to do so, the Company
is authorized to withhold from any cash or Stock remuneration then or thereafter
payable to Employee any tax required to be withheld by reason of such resulting
compensation income. Employee shall have the right to determine whether money or
shares of Stock shall be delivered to the Company. Upon an exercise of this
Option, the Company is further authorized in its discretion to satisfy any such
withholding requirement out of any cash or shares of Stock distributable to
Employee upon such exercise.

     5.   STATUS OF STOCK.  Notwithstanding any other provision of this
          ---------------                                              
Agreement, in the absence of an effective registration statement for issuance
under the Securities Act of 1933, as amended (the 'Act'), of the shares of Stock
acquirable upon exercise of this Option, or an available exemption from
registration under the Act, issuance of shares of Stock acquirable upon exercise
of this Option will be delayed until registration of such shares is effective or
an exemption from registration under the Act is available. The Company intends
to use its best efforts to ensure that no such delay will occur in the event
exemption from registration under the Act is available upon an exercise of this
Option, Employee (or the person permitted to exercise this Option in the event
of Employee's death or incapacity), if requested by the Company to do so, will
execute and deliver to the Company in writing an agreement containing such
provisions as the Company may require to assure compliance with applicable
securities laws.

     Employee agrees that the shares of Stock which Employee may acquire by
exercising this Option will not be sold or otherwise disposed of in any manner
which would constitute a violation of any applicable securities laws, whether
federal or state.  Employee also agrees (i) that the certificates representing
the shares of Stock purchased under this Option may bear such legend or legends
as the Company deems appropriate in order to assure compliance with applicable
securities laws, (ii) that the Company may refuse to register the transfer of
the shares of Stock purchased under this Option on the stock transfer records of
the Company if such proposed transfer would in the opinion of counsel
satisfactory to the Company constitute a violation of any applicable securities
law and (iii) that the Company may give related instructions to its transfer
agent, if any, to stop registration of the transfer of the shares of Stock
purchased under this Option.

     If Employee desires to sell any shares of Stock acquired pursuant to the
provisions of this Agreement and if such shares may not be sold on the open
market without registration pursuant to applicable securities laws, then the
Company shall, within five days after notice from Employee indicating his
intention to sell such shares and the number of shares to be sold, purchase for
cash such shares at a price per share based on the closing sales price for
shares of Stock traded on the New York Stock Exchange on the date of receipt by
the Company of said notice.

     6.   EMPLOYMENT RELATIONSHIP.  For purposes of this Agreement, Employee
          -----------------------                                           
shall be considered to be in the employment of the Company as long as Employee
remains an employee of either the Company, a parent or subsidiary corporation
(as defined in section 424 of the Code) of the Company, or a corporation or a
parent or subsidiary of such

                                       4

 
corporation assuming or substituting a new option for this Option. Any question
as to whether and when there has been a termination of such employment, and the
cause of such termination, shall be determined by the Committee or its delegate,
as appropriate, and such determination shall be final.

     7.   BINDING EFFECT.  This Agreement shall be binding upon and inure to the
          --------------                                                        
benefit of any successors to the Company and all persons lawfully claiming under
Employee.

     8.   GOVERNING LAW.  This Agreement shall be governed by, and construed in
          -------------                                                        
accordance with, the laws of the State of Texas excluding any conflict-of-law
rule or principle that might refer to the laws of another State or country.

     IN WITNESS WHEREOF, the Company has caused this Agreement to be duly
executed by its officer thereunto duly authorized, and Employee has executed
this Agreement, all as of the day and year first above written.

                                            HALLIBURTON COMPANY

                                            By:
                                            Name: ____________________________
                                            Title: ___________________________



                                            __________________________________
                                            Melvin N. Miller
                                            Employee


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