EXHIBIT 8.1

            [LETTERHEAD OF WINSTEAD SECHREST & MINICK APPEARS HERE]

                                August 30, 1996

Board of Directors
Landmark Graphics Corporation
15150 Memorial Drive
Houston, Texas 77079-4304

Gentlemen:

     We have acted as counsel to Landmark Graphics Corporation, a Delaware
corporation (the "Company"), in connection with the merger (the "Merger") of the
Company with and into Halliburton Acq. Company (the "Merger Sub"), a Delaware
corporation and a wholly-owned subsidiary of Halliburton Company, a Delaware
corporation (the "Acquiror"), pursuant to that certain Agreement and Plan of
Merger, dated as of June 30, 1996, by and among the Acquiror, the Merger Sub and
the Company (the "Merger Agreement"), and the agreements, documents and
instruments contemplated in the Merger Agreement.

     In rendering the opinions expressed below, we have examined, and are
relying upon, the completeness, truth and accuracy, at all relevant times, of
the following:

     1.   the Merger Agreement;

     2.   the Registration Statement on Form S-4 filed by the Acquiror with the
Securities and Exchange Commission pursuant to the Securities Act of 1933 in
conjunction with the Merger (the "Registration Statement");

     3.   that certain Stock Option Agreement (the "Option Agreement"), dated
June 30, 1996, by and between the Company and the Acquiror;

     4.   that certain Voting Agreement, dated June 30, 1996, by and among the
Acquiror, S. Rutt Bridges and Barbara Ann Bridges;

     5.   that certain Rights Agreement (the "Rights Agreement"), dated
September 1, 1995, by and between the Company and Chemical Bank;

     6.   that certain First Amendment to the Rights Agreement, dated June 30,
1996, by and between the Company and Chemical Bank;

 
Board of Directors
August 30, 1996
Page 2

     7.   the Company's Disclosure Letter (as defined in the Merger Agreement);

     8.   the Acquiror's Disclosure Letter (as defined in the Merger Agreement);

     9.   the certificates of incorporation and such other corporate records,
documents and certificates of the Acquiror, the Merger Sub and the Company as in
our judgment are necessary or desirable to enable us to render the opinions
expressed herein; and

     10.  certificates containing the following representations made to us by
the Acquiror, the Merger Sub and/or the Company:

          (i) The Merger Agreement and the agreements, documents and instruments
     contemplated thereby contain all material terms of the Merger and there are
     no agreements or documents which amend, modify or revise the provisions of
     the Merger Agreement or the agreements, documents or instruments
     contemplated thereby or amend, modify or revise the terms of the Merger or
     the consideration to be received by the stockholders of the Company in
     connection with the Merger.

          (ii) To the knowledge of the Company, the stockholders of the Company
     are not under any binding contract or commitment requiring them to sell any
     of the shares of common stock of the Acquiror to be received pursuant to
     the Merger.  The stockholders of the Company do not have any plan or intent
     to sell or otherwise dispose of more than fifty percent (50%) of the shares
     of common stock of the Acquiror to be received pursuant to the Merger.

          (iii)  After the Merger, the Merger Sub will continue to be a wholly
     owned subsidiary of the Acquiror with substantially the same business as is
     currently being conducted by the Company, and the Merger Sub and the
     Acquiror have no plan or intention to sell or otherwise dispose of the
     capital stock of the Merger Sub, to liquidate the Merger Sub, or to cause
     the Merger Sub to sell or otherwise dispose of any of the Merger Sub's
     assets except for dispositions in the ordinary course of business.

          (iv) The Company has not paid extraordinary dividends to any
     stockholders, made material payments to any stockholder in redemption of
     all or a portion of the stockholder's equity interest in the Company, or
     transferred assets pursuant to a tax-free spin-off during the two-year
     period ending on the date hereof.

          (v) The Acquiror, the Merger Sub, the Company and the stockholders of
     the Company will pay their respective expenses related to the Merger, if
     any.

          (vi) Pursuant to the Merger, the Merger Sub will acquire 100% of the
     assets of the Company.

 
Board of Directors
August 30, 1996
Page 3

          (vii)  Immediately after the Merger, the Merger Sub will own assets
     representing at least 90% of the fair market value of the Company's net
     assets and at least 70% of the fair market value of the Company's gross
     assets held immediately before and in contemplation of the Merger.

          (viii)  The method of converting shares of the Company's common stock
     into shares of the Acquiror's common stock set forth in the Merger
     Agreement is a result of arm's length negotiations. Accordingly, at the
     time the method of exchange was determined and at all relevant times
     thereafter, the aggregate fair market value of the shares of the Acquiror's
     common stock to be received by the Company stockholders in exchange for the
     Company's common stock was approximately equal to the fair market value of
     the shares of the Company's common stock to be surrendered in exchange
     therefor.

          (ix) The Merger Sub has no liabilities.

          (x) There is no intercorporate indebtedness between (i) the Acquiror
     and the Company, or (ii) the Merger Sub and the Company, which was issued
     or acquired or will be settled at a discount.

          (xi) The terms of the Merger Agreement providing for the payment of
     cash in lieu of fractional share interests are solely for the purpose of
     saving the Acquiror the expense and inconvenience of issuing and
     transferring the fractional share interests and such payment is not
     separately bargained for consideration.

          (xii)  There is no plan or intention on the part of the Acquiror to
     redeem or otherwise reacquire any of the Acquiror's common stock to be
     issued pursuant to the Merger.

          (xiii)  No capital stock of the Merger Sub will be issued to the
     Company or the stockholders of the Company in connection with the Merger.

          (xiv)  Compensation, if any, to be paid by the consolidated Merger
     Sub/Company entity to stockholder/employees of the Company will be for
     services actually rendered and will be commensurate with amounts paid to
     third parties bargaining at arm's length for similar services, and no part
     of such compensation represents consideration for their shares of the
     Company's common stock.

          (xv) Except for cash received in lieu of fractional shares,
     stockholders of the Company shall receive solely voting common stock of the
     Acquiror in exchange for their shares of the Company's common stock
     pursuant to the Merger.

 
Board of Directors 
August 30, 1996
Page 4

          (xvi)  The business purposes of the Merger are those set forth in the
     Registration Statement.

          (xvii)  Substantially more than 50% in value of the assets of the
     Company consist of assets which are not capital stock or securities held
     for investment and substantially more than 20% of the Company's assets are
     not held for investment.

          (xviii)  Except as set forth in the Option Agreement, the Rights
     Agreement, and the Merger Agreement, as of the date hereof the Company does
     not have outstanding any warrants, options, convertible securities or any
     other type of right pursuant to which any person could acquire capital
     stock in the Company.

          (xix)  The Acquiror does not own, nor has it owned during the past
     five years, any shares of the capital stock of the Company.

          (xx) On the date hereof, the fair market value of the assets of the
     Company exceeds the sum of the Company's liabilities, plus the amount of
     liabilities, if any, to which such assets are subject.

          (xxi)  On the date hereof, the fair market value of the assets of  the
     Merger Sub exceeds the sum of the Merger Sub's liabilities, plus the amount
     of liabilities, if any, to which such assets are subject.

          (xxii)  Neither the Merger Sub nor the Company is under the
     jurisdiction of a court in a Title 11 or similar case within the meaning of
     (S)368(a)(3)(A) of the Internal Revenue Code of 1986, as amended (the
     "Code").

          (xxiii)  Neither the Acquiror nor the Merger Sub has any plan or
     intention to cause the Merger Sub to issue any capital stock in such amount
     as would cause the Acquiror to fail to be in control (as defined in
     (S)368(c) of the Code) of the Merger Sub after the Merger.

     In connection with rendering this opinion, we have assumed to be true and
are relying upon, without any independent investigation or review thereof, the
following:

     1.   The authenticity of all documents submitted to us as originals, the
conformity to original documents of all documents submitted to us as copies, and
the authenticity of the originals of such documents.

     2.   The genuineness of all signatures, the due authorization, execution
and delivery of all documents by all parties thereto and the due authority of
all persons executing such documents.

 
Board of Directors
August 30, 1996
Page 5

     Based on our examination of the foregoing items and subject to the
assumptions, limitations, qualifications and representations set forth herein,
and based on the provisions of the Code and the treasury regulations,
administrative pronouncements and rulings promulgated thereunder, we are of the
opinion that:

     1.   The Merger will constitute a "reorganization" within the meaning of
(S)368(a) of the Code.

     2.   The Company, the Acquiror and the Merger Sub will each be a "party" to
the reorganization within the meaning of (S) 368(b) of the Code.

     3.   No gain or loss (except with respect to cash received in lieu of
fractional shares) will be recognized by holders of shares of the Company's
common stock on the exchange of their shares solely for shares of the Acquiror's
common stock pursuant to the Merger.  Section 354(a) of the Code.

     4.   The tax basis of the shares of the Acquiror's common stock received by
the holders of shares of the Company's common stock will be the same as the tax
basis of the shares of the Company's common stock exchanged therefor, decreased
by the amount of any cash received and increased by the amount of any gain
recognized on the exchange.  Section 358 of the Code.

     5.   The holding period of shares of the Acquiror's common stock received
by a holder of shares of the Company's common stock will include the holding
period of the shares of the Company's common stock exchanged therefor, provided
that such shares of the Company's common stock were held by such holder as
capital assets on the date of the consummation of the Merger.  Section 1223 of
the Code.

     In addition to the matters set forth above, this opinion is subject to the
following exceptions, limitation and qualifications:

     1.   Our opinions expressed herein are based upon our interpretation of the
existing provisions of the Code and existing judicial decisions, administrative
regulations, revenue rulings and revenue procedures.  Our opinions are not
binding upon the Internal Revenue Service or the courts and there is no
assurance that the Internal Revenue Service will not challenge the conclusions
set forth herein.  No assurance can be given that future legislative, judicial
or administrative changes, on either a prospective or retroactive basis, will
not adversely affect the accuracy of the opinions stated herein.  We undertake
no obligation to advise you of changes in law which may occur after the date
hereof.

     2.   Our opinions are limited to the United States federal income tax
matters addressed herein, and no other opinions are rendered with respect to any
other matter not specifically set forth in the foregoing opinions.

 
Board of Directors
August 30, 1996
Page 6


     If any one of the statements, representations or assumptions we have relied
upon to issue this opinion is incorrect in any material respect, our opinion
might be adversely affected and may not be relied upon.

     These opinions are solely for your benefit and may not be relied upon in
any manner by any other person or entity.

                              WINSTEAD SECHREST & MINICK P.C.



                              By: /s/ THOMAS R. HELFAND
                                 -----------------------------
                                 Thomas R. Helfand