EXHIBIT 10.1

                        EXECUTIVE EMPLOYMENT AGREEMENT


     This Executive Employment Agreement ("Agreement"), including the attached
Exhibit "A", is entered into by and between Landmark Graphics Corporation, a
Delaware corporation having offices at 15150 Memorial, Houston, Texas 77079-4304
("Employer"), Halliburton Company, a Delaware corporation having offices at 3600
Lincoln Plaza, 500 N. Akard Street, Dallas, Texas 75201-3391 ("Halliburton"),
and Robert P. Peebler, an individual currently residing at 5607 Court of Lions,
Houston, Texas 77069 ("Employee"), to be effective at the effective date that
Employer becomes a wholly owned 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 wholly
owned 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 wholly-owned 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 1:  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, 1999 ( the "Term"), subject to the terms and conditions of this
Agreement.

     1.2.  Beginning as of the Effective Date, Employee shall be employed as
Chief Executive Officer and 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 reasonable policies and procedures as Employer may
establish from time to time.

     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 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 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 Employer's Board of Directors in accordance with the
Employer'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 other corporations' 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 Employer's Board of Directors any facts which might involve a possible
conflict of interest.

     1.5.  Employee represents that he is not aware of any pre-existing health
problems that may materially impair his ability to perform his responsibilities
hereunder which have not been disclosed to Employer and Halliburton.

ARTICLE 2:  COMPENSATION AND BENEFITS

     2.1.  Employee's base salary during the Term shall be not less than
$400,000.00 per annum which shall be paid in accordance with the Employer's
standard payroll practice for its executives.

     2.2  Beginning January 1, 1997 and continuing for the remainder of the
Term, Employee shall participate in the Halliburton Energy Services CVA
Performance Pay Plan in the same participant category as the Executive Vice-
President and Chief Operating Officer of Halliburton Energy Services.

     2.3.  As of the Effective Date, Halliburton shall grant to Employee under
the Halliburton Company 1993 Stock and Long-Term Incentive Plan a nonqualified
stock option to purchase up to 20,000 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.

                        EXECUTIVE EMPLOYMENT AGREEMENT
                                      -2-

 
     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.  At all times during 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 1997, 1998, and
1999, Employee will receive an allocation of at least $100,000.00 to his
Deferred Compensation Account thereunder at the end of each such full calendar
year provided he was employed by the 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 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 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.  Employer shall not 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.

                        EXECUTIVE EMPLOYMENT AGREEMENT
                                      -3-

 
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.

     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" (as hereinafter defined), 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 or Halliburton'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
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 reduction in Employees' rank, material reduction in his
responsibility with Employer or requirement for Employee to relocate outside of
the Houston, Texas metropolitan area.  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; or (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.  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, Employee shall have the right to
immediately exercise all outstanding stock options and Employer shall pay to
Employee a severance benefit consisting of a 

                        EXECUTIVE EMPLOYMENT AGREEMENT
                                      -4-

 
single lump sum cash payment of $800,000.00. Such severance benefit shall be
paid no later than sixty (60) days following Employee's termination of
employment. 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 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 (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.

                        EXECUTIVE EMPLOYMENT AGREEMENT
                                      -5-

 
     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. The above 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.  Employee agrees that during the period of
Employee's non-competition obligations hereunder, Employee will not, directly or
indirectly for Employee or for others, in any geographic area or market where
Employer or any of their affiliated companies are conducting any business (other
than de minimis business operations) as of the date of termination of the
employment relationship or have during the previous twelve months conducted any
business (other than de minimis business operations):

     (i)   engage in any business directly competitive with any business (other
           than de minimis business operations) conducted by Employer;

                        EXECUTIVE EMPLOYMENT AGREEMENT
                                      -6-

 
     (ii)  render advice or services to, or otherwise assist, any other person,
           association, or entity who is engaged, directly or indirectly, in any
           business directly competitive with any business (other than de
           minimis business operations) conducted by Employer; or

     (iii) induce any employee of Employer(other than Employee's personal
           secretary or administrative assistant) to terminate his employment
           with Employer, or hire or assist in the hiring of any such induced
           employee by any person, association, or entity not affiliated with
           Employer.

These non-competition obligations shall extend until two years after termination
of the employment relationship between Employer and Employee.  The above
notwithstanding, nothing in this Section 5.1 shall prohibit Employee from
engaging in or being employed by any entity that engages in the provision of
management consulting or other consulting services to third parties, even where
such entity on occasion renders advice or services to, or otherwise assists, any
other person, association, or entity who is engaged, directly or indirectly, in
any business directly competitive with any business conducted by Employer or any
of Employer's affiliates, so long as Employee does not personally, directly or
indirectly (A) participate in rendering such advice, services or assistance to
any such competing person, association or entity, (B) provide any information or
other assistance to any other person employed by Employee or by any such
consulting entity for use, directly or indirectly, in rendering such assistance
to any competing person, association or entity or (C) engage in any conduct
which would be violative of the provisions of Article 4 hereof.

     5.2. Employee understands that the foregoing restrictions may limit his
ability to engage in certain businesses anywhere in the world during the period
provided for above, but acknowledges that Employee will receive sufficiently
high remuneration and other benefits under this Agreement to justify such
restriction.  Employee acknowledges that money damages would not be sufficient
remedy for any breach of this Article 5 by Employee, and agrees that Employer,
on its own behalf or on behalf of any of its affiliates, shall be entitled to
specific performance and injunctive relief as remedies for such breach or any
threatened breach.  Such remedies shall not be deemed the exclusive remedies for
a breach of this Article 5, but shall be in addition to all remedies available
at law or in equity to Employer, including, without limitation, the recovery of
damages from Employee and his agents involved in such breach.

     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 therein set
forth to be modified by such courts so as to be reasonable and enforceable and,
as so modified by the court, to be fully enforced.

                        EXECUTIVE EMPLOYMENT AGREEMENT
                                      -7-

 
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 or in which Employer has a 50% or more equity interest, and (ii) any
action or omission permitted to be taken or omitted by Employer hereunder shall
only be taken or omitted by Employer upon the express authority of the Board of
Directors of Employer or of any Committee of the Board 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 wholly owned subsidiary of
Halliburton and shall not become effective until such time as the Employer has
become a wholly owned 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
State of Texas, excluding any conflict-of-law rule or principle that might refer
to the laws of another State or country.

     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
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.

                        EXECUTIVE EMPLOYMENT AGREEMENT
                                      -8-

 
     6.7.      This Agreement shall be binding upon and inure to the benefit of
Employer 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. This Agreement upon the effectiveness of the merger of Employer into
Halliburton replaces and merges any previous agreements and discussions
pertaining to the subject matter covered herein including the Change In Control
Agreement dated October 19, 1995 between Employer and Employee; provided,
however, that the provisions of Section 5(a)(v)(A) of the Change in Control
Agreement dated October 19, 1995 between Employer and Employee and the
Indemnification Agreement dated November 21, 1990 between Employer and Employee
shall survive and shall remain in effect without regard to the provisions of
this Agreement.  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.

     6.9  Halliburton has executed this agreement in its capacity as sponsor of
the Halliburton employee benefit plans, programs and stock option plans in which
Employee is entitled to participate pursuant to this Agreement.

                        EXECUTIVE EMPLOYMENT AGREEMENT
                                      -9-

 
     IN WITNESS WHEREOF, Employer, Halliburton and Employee have duly executed
this Agreement at Houston, Texas in multiple originals to be effective on the
date first stated above.

                              LANDMARK GRAPHICS CORPORATION


                              By: /s/ WILLIAM H. SEIPPEL
                                 -----------------------------------------
                              Name: William H. Seippel
                                   ---------------------------------------
                              Title: VP & CFO
                                    --------------------------------------


                              HALLIBURTON COMPANY


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

                              EMPLOYEE

                              /s/ ROBERT P. PEEBLER
                              --------------------------------------------
                              Name: Robert P. Peebler

Date:  June 30, 1996

                        EXECUTIVE EMPLOYMENT AGREEMENT
                                      -10-

 
                                  Exhibit A to
                         Executive Employment Agreement
                       By and Between Robert P. Peebler,
             Landmark Graphics Corporation and Halliburton Company


                      NONSTATUTORY STOCK OPTION AGREEMENT

     AGREEMENT made as of the ___ day of ________, 1996 between HALLIBURTON
COMPANY, a Delaware corporation (the "Company"), and Robert P. Peebler
("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 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
20,000 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:



                               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 Committee administering the Plan (the "Committee")), 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 is terminated by the
     Company other than for "Cause" or Employee terminates his employment with
     the Company (i) because of a material breach by the Company of any material
     provision of any employment agreement between the Company and Employee
     which remains uncorrected for 30 days following written notice of such
     breach by Employee to the Company or (ii) within six months of a reduction
     in Employee's rank, a material reduction in his responsibilities with the
     Company or requirement for Employee to relocate outside the Houston, Texas
     metropolitan area, this Option may be exercised in full by Employee at any
     time during 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. For purposes of this Agreement, 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; or (iii) Employee's material
     breach of any material provision of this Agreement which remains
     uncorrected for 30 days following written notice to Employee by the Company
     of such breach which specifies the basis for the breach in detail. No act
     or failure to act 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 the Company. If Employee's employment
     with Company is terminated for any reason set forth in this subparagraph
     within six months from 

                                      -2-

 
     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.

          (d) If Employee's employment with the Company terminates for any
     reason other than those set forth in subparagraphs (a) through (c) 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 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.
                                      -3-

 
     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 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.

                                      -4-

 
     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:__________________________________


                                      ________________________________________ 
                                          Robert P. Peebler
                                          Employee

                                      -5-