Exhibit 5.1



                                 VINSON & ELKINS
                                ATTORNEYS AT LAW

                             VINSON & ELKINS L.L.P.
                              2300 FIRST CITY TOWER
                               1001 FANNIN STREET
                            HOUSTON, TEXAS 77002-6760
                            TELEPHONE (713) 758-2222
                               FAX (713) 758-2346


                                November 30, 2001

Halliburton Company
3600 Lincoln Plaza
500 North Akard Street
Dallas, Texas  75201

Ladies and Gentlemen:

         We have acted as counsel for Halliburton Company, a Delaware
corporation (the "Company"), with respect to certain legal matters in connection
with the registration by the Company and Halliburton Capital Trust I, a Delaware
statutory business trust (the "Trust"), under the Securities Act of 1933 (the
"Securities Act"), of the offer and sale from time to time, pursuant to Rule 415
under the Securities Act, (a) by the Company of (i) unsecured debt securities,
in one or more series, consisting of notes, debentures or other evidences of
indebtedness (the "Debt Securities"), (ii) shares of common stock of the Company
(the "Common Stock"), (iii) stock purchase contracts (the "Stock Purchase
Contracts") to purchase shares of Common Stock or other securities of the
Company at a future date, (iv) stock purchase units (the "Stock Purchase Units")
consisting of a Stock Purchase Contract and debt securities, preferred
securities, warrants or debt obligations of third parties securing the holders'
obligations to purchase the securities under the Stock Purchase Contracts, (v)
shares of preferred stock of the Company, in one or more series (the "Preferred
Stock"), which may be issued in the form of depositary shares evidenced by
depositary receipts (the "Depositary Shares"), (vi) securities warrants (the
"Warrants") to purchase Debt Securities, Preferred Stock, Depositary Shares or
Common Stock, (vii) a guarantee of the Trust's Preferred Securities (the
"Preferred Securities Guarantee") and (viii) in addition to the Debt Securities,
subordinated debentures or junior subordinated debentures (each, as applicable,
the "Trust Debentures") to be purchased by the Trust with the proceeds from the
sale of preferred securities (the "Preferred Securities"), and (b) by the Trust
of the Trust's Preferred Securities. The Company has advised us that the
aggregate initial offering prices of the Debt Securities, Preferred Stock,
Depositary Shares, Common Stock, Warrants, Stock Purchase Contracts, Stock
Purchase Units and Preferred

HOUSTON AUSTIN BEIJING DALLAS LONDON MOSCOW NEW YORK SINGAPORE WASHINGTON, D.C.




Halliburton Company
Page 2
November 30, 2001

Securities (excluding the aggregate initial offering price of the Trust
Debentures) offered by the Company and the Trust (collectively, including the
Trust Debentures, the "Securities") will not exceed $1,000,000,000 or, if
applicable, the equivalent thereof in any other currency or currency unit. The
Company has advised us that the Securities will be offered in amounts, at prices
and on terms to be determined in light of market conditions at the time of sale
and to be set forth in supplements to the Prospectus contained in the
Registration Statement on Form S-3 of the Company and the Trust to which this
opinion is an exhibit.

          We have examined originals or copies, certified or otherwise
identified to our satisfaction, of (i) the Restated Certificate of Incorporation
and Bylaws of the Company, each as amended to the date hereof; (ii) the Second
Senior Indenture dated as of December 1, 1996, between the predecessor to the
Company and Texas Commerce Bank National Association (now JPMorgan Chase Bank, a
New York banking corporation), as trustee (the "Trustee"), as supplemented and
amended by the First Supplemental Indenture dated as of December 5, 1996,
between the predecessor to the Company and the Trustee, the Second Supplemental
Indenture dated as of December 12, 1996, between the predecessor to the Company
and the Trustee, the Third Supplemental Indenture dated as of August 1, 1997,
between the Company and the Trustee, and the Fourth Supplemental Indenture dated
as of September 29, 1998, between the Company and the Trustee (the "Senior
Indenture"); (iii) the Subordinated Indenture dated as of January 2, 1991,
between the predecessor to the Company and the Trustee, as supplemented and
amended by the First Supplemental Indenture dated as of December 12, 1996,
between the Company and the Trustee (the "Subordinated Indenture"); (iv) the
Junior Subordinated Indenture dated November 29, 2001 between the Company and
the Trustee (the "Junior Subordinated Indenture," and together with the Senior
Indenture and the Subordinated Indenture, the "Indentures," and each, an
"Indenture"); (v) a form of the Preferred Securities Guarantee to be entered
into by the Company, in the form included as an exhibit to the Registration
Statement; (vi) the Certificate of Trust and Declaration of Trust of the Trust;
and (vii) such other certificates, statutes and other instruments and documents
as we considered appropriate for purposes of the opinions hereafter expressed.
In addition, we reviewed such questions of law as we considered appropriate.

         As to any facts material to our opinion, we have made no independent
investigation of such facts and have relied, to the extent that we deem such
reliance proper, upon certificates of public officials and officers or other
representatives of the Company.

         In rendering the opinions set forth below, we have assumed that (i) all
information contained in all documents reviewed by us is true and correct; (ii)
all signatures on all documents examined by us are genuine; (iii) all documents
submitted to us as originals are authentic and all documents submitted to us as
copies conform to the originals of those documents; (iv) each natural person
signing any document reviewed by us had the legal capacity to do so; (v) each
person signing in a representative capacity (other than on behalf of the
Company) any document reviewed by us had authority to sign in such capacity;
(vi) the Registration Statement, and any amendments thereto (including
post-effective amendments) will have become effective and comply with all
applicable laws; (vii) a prospectus supplement will have been prepared and filed



Halliburton Company
Page 3
November 30, 2001

with the Securities and Exchange Commission describing the Securities offered
thereby; (viii) all Securities will be issued and sold in compliance with
applicable federal and state securities laws and in the manner stated in the
Registration Statement and the applicable prospectus supplement; (ix) the Senior
Indenture, the Subordinated Indenture and the Junior Subordinated Indenture,
together with any supplemental indenture or other instruments establishing a
series of Debt Securities or Trust Debentures, as the case may be, to be issued
under any of the Indentures, will each be duly authorized, executed and
delivered by the parties thereto in substantially the form reviewed by us or
with changes that do not affect the opinions given hereunder; (x) a definitive
purchase, underwriting or similar agreement with respect to any Securities
offered will have been duly authorized and validly executed and delivered by the
Company and the other parties thereto; and (xi) any Securities issuable upon
conversion, exchange or exercise of any Security being offered will have been
duly authorized, created and, if appropriate, reserved for issuance upon such
conversion, exchange or exercise.

         Based on the foregoing, and subject to the assumptions, qualifications,
limitations and exceptions set forth herein, we are of the opinion that:

         1.  With respect to Debt Securities to be issued under the Senior
Indenture, when (i) the Board of Directors of the Company (or a committee
thereof) has taken all necessary corporate action to approve the issuance and
terms of the Debt Securities, the terms of the offering thereof and related
matters; (ii) the terms of the Debt Securities and of their issuance and sale
have been established so as not to violate any applicable law or result in a
default under or breach of any agreement or instrument binding upon the Company
and so as to comply with any requirement or restriction imposed by any court or
governmental body having jurisdiction over the Company; and (iii) the Debt
Securities have been duly executed, authenticated, issued and delivered in
accordance with the provisions of the Senior Indenture and in accordance with
the applicable definitive purchase, underwriting or similar agreement approved
by the Board of Directors of the Company (or a committee thereof), then upon
payment of the consideration provided for therein, the Debt Securities will be
legally issued and will constitute valid and binding obligations of the Company,
enforceable against the Company in accordance with their terms and will be
entitled to the benefits of the Senior Indenture.

         2.  With respect to Debt Securities to be issued under the Subordinated
Indenture, when (i) the Board of Directors of the Company (or a committee
thereof) has taken all necessary corporate action to approve the issuance and
terms of the Debt Securities, the terms of the offering thereof and related
matters; (ii) the terms of the Debt Securities and of their issuance and sale
have been established so as not to violate any applicable law or result in a
default under or breach of any agreement or instrument binding upon the Company
and so as to comply with any requirement or restriction imposed by any court or
governmental body having jurisdiction over the Company; and (iii) the Debt
Securities have been duly executed, authenticated, issued and delivered in
accordance with the provisions of the Subordinated Indenture and in accordance
with the applicable definitive purchase, underwriting or similar agreement
approved by the Board of Directors of the Company (or a committee thereof), then
upon payment of the consideration provided for therein, the Debt Securities will
be legally issued and will constitute




Halliburton Company
Page 4
November 30, 2001

valid and binding obligations of the Company, enforceable against the Company in
accordance with their terms and will be entitled to the benefits of the
Subordinated Indenture.

         3.  With respect to Debt Securities to be issued under the Junior
Subordinated Indenture, when (i) the Board of Directors of the Company (or a
committee thereof) has taken all necessary corporate action to approve the
issuance and terms of the Debt Securities, the terms of the offering thereof and
related matters; (ii) the terms of the Debt Securities and their issuance and
sale and the terms of the Junior Subordinated Indenture have been established so
as not to violate any applicable law or result in a default under or breach of
any agreement or instrument binding upon the Company and so as to comply with
any requirement or restriction imposed by any court or governmental body having
jurisdiction over the Company; and (iii) the Debt Securities have been duly
executed, authenticated, issued and delivered in accordance with the provisions
of the Junior Subordinated Indenture and in accordance with the applicable
definitive purchase, underwriting or similar agreement approved by the Board of
Directors of the Company (or a committee thereof), then upon payment of the
consideration provided for therein, the Debt Securities will be legally issued
and will constitute valid and binding obligations of the Company, enforceable
against the Company in accordance with their terms and will be entitled to the
benefits of the Junior Subordinated Indenture.

         4.  With respect to Common Stock, when (i) the Board of Directors of
the Company (or a committee thereof) has taken all necessary corporate action to
approve the creation of and the issuance and terms of the Common Stock, the
terms of the offering thereof and related matters and (ii) the Common Stock or
certificates representing the Common Stock have been duly executed,
countersigned, registered and delivered in accordance with the applicable
definitive purchase, subscription, underwriting or similar agreement approved by
the Board of Directors of the Company (or a committee thereof), then upon
payment of the consideration provided for therein, the Common Stock will be
legally issued.

         5.  With respect to Stock Purchase Contracts, when (i) the purchase
agreement for the Stock Purchase Contracts has been duly authorized and validly
executed by the parties thereto; (ii) the Board of Directors of the Company (or
a committee thereof) has taken all necessary corporate action to approve and
establish the terms of the Stock Purchase Contracts and to authorize and approve
the issuance thereof, the terms of the offering and related matters; and (iii)
the Stock Purchase Contracts have been duly executed and delivered in accordance
with the purchase agreement and the applicable definitive purchase, underwriting
or similar agreement approved by or on behalf of the Board of Directors of the
Company (or a committee thereof), then upon payment of the consideration
therefore provided for therein, the Stock Purchase Contracts will be legally
issued.

         6.  With respect to Stock Purchase Units, when (i) the purchase
agreement for the Stock Purchase Units has been duly authorized and validly
executed by the parties thereto, (ii) the Board of Directors of the Company (or
a committee thereof) has taken all necessary corporate action to approve and
establish the terms of the Stock Purchase Units and to authorize and approve the
issuance thereof, the terms of the offering and related matters; and (iii) the
Stock Purchase Units have been duly executed and delivered in accordance with
the purchase



Halliburton Company
Page 5
November 30, 2001

agreement and the applicable definitive purchase, underwriting or similar
agreement approved by or on behalf of the Board of Directors of the Company (or
a committee thereof), then upon payment of the consideration therefor provided
therein, the Stock Purchase Units will be legally issued.

         7.  With respect to Preferred Stock, when (i) the Board of Directors of
the Company (or a committee thereof) has taken all necessary corporate action to
approve the creation of and the issuance and terms of the Preferred Stock, the
terms of the offering thereof and related matters and (ii) the Preferred Stock
or certificates representing the Preferred Stock have been duly executed,
countersigned, registered and delivered in accordance with the applicable
definitive purchase, subscription, underwriting or similar agreement approved by
the Board of Directors of the Company (or a committee thereof), then upon
payment of the consideration provided for therein, the Preferred Stock will be
legally issued.

         8.  With respect to the Warrants, when (i) the Board of Directors of
the Company (or a committee thereof) has taken all necessary corporate action to
approve the creation of and the issuance and terms of the Warrants, the terms of
the offering thereof and related matters; (ii) the warrant agreement or
agreements relating to the Warrants have been duly authorized and validly
executed and delivered by the Company and the warrant agent appointed by the
Company; and (iii) the Warrants or certificates representing the Warrants have
been duly executed, countersigned, registered and delivered in accordance with
the appropriate warrant agreement or agreements and the applicable definitive
purchase, underwriting or similar agreement approved by the Board of Directors
of the Company (or a committee thereof), then upon payment of the consideration
provided for therein, the Warrants will be legally issued.

         9.  With respect to the Preferred Securities Guarantee, when (i) the
Preferred Securities Guarantee has been duly authorized, executed and delivered
by the Company to the guarantee trustee; (ii) the Board of Directors of the
Company (or a committee thereof) has taken all necessary corporate action to
approve and establish the terms of the Preferred Securities Guarantee and to
authorize and approve the issuance thereof, the terms of the offering and
related matters; and (iii) the Preferred Securities Guarantee has been duly
executed, issued and delivered in accordance with the resolutions of the Board
of Directors of the Company (or a committee thereof), then upon payment for and
delivery of the Preferred Securities in accordance with the applicable purchase
agreement, the Preferred Securities Guarantee will constitute a valid and
binding obligation of the Company, enforceable against the Company in accordance
with its terms.

        10.  With respect to Trust Debentures, when (i) either (a) each of the
conditions set forth in paragraph 2 above have been satisfied (if the Trust
Debentures are issued under the Subordinated Indenture) or (b) each of the
conditions set forth in paragraph 3 above have been satisfied (if the Trust
Debentures are issued under the Junior Subordinated Indenture) (ii) the Board of
Directors of the Company (or a committee thereof) has taken all necessary
corporate action to approve the issuance and terms of any Trust Debentures, the
terms of the offering thereof and related matters, (iii) the terms of the Trust
Debentures and their issuance and sale have been duly established so as not to
violate any applicable law or result in a default under or



Halliburton Company
Page 6
November 30, 2001

breach of any agreement or instrument binding upon the Company and so as to
comply with any requirement or restriction imposed by any court or governmental
body jurisdiction over the Company, and (iv) the Trust Debentures have been duly
executed, authenticated, issued and delivered in accordance with the provisions
of the Subordinated Indenture or Junior Subordinated Indenture, as applicable,
and in accordance with the applicable definitive purchase agreement,
underwriting or similar agreement approved by the Board of Directors (or a
committee thereof), then upon payment of the consideration provided for therein,
the Trust Debentures will be legally issued and will constitute valid and
binding obligations of the Company, enforceable against the Company in
accordance with their terms and will be entitled to the benefits of the
Subordinated Indenture or Junior Subordinated Indenture, as applicable.

         The foregoing opinions are qualified to the extent that the
enforceability of any document, instrument or Security may be limited by or
subject to (i) bankruptcy, insolvency, fraudulent transfer or conveyance,
reorganization, moratorium or other similar laws relating to or affecting
creditors' rights generally, and general equitable or public policy principles,
and (ii) with respect to any Debt Securities denominated in a currency other
than United States dollars, the requirement that a claim (or a foreign currency
judgment in respect of such a claim) with respect to such Securities be
converted to United States dollars at a rate of exchange prevailing on a date
determined pursuant to applicable law or governmental authority.

         We express no opinions concerning (i) the validity or enforceability of
any provisions contained in Indentures that purport to waive or not give effect
to rights to notices, defenses, subrogation or other rights or benefits that
cannot be effectively waived under applicable law or (ii) the enforceability of
indemnification provisions to the extent they purport to relate to liabilities
resulting from or based upon negligence or any violation of federal or state
securities or blue sky laws.

         The foregoing opinions are limited in all respects to the laws of the
Delaware General Corporation Law (including the applicable provisions of the
Delaware Constitution and the reported judicial decisions interpreting these
laws) and the laws of the State of New York and the federal law of the United
States of America, and we do not express any opinions as to the laws of any
other jurisdiction.

         We hereby consent to the filing of this opinion as an exhibit to the
Registration Statement. By giving such consent, we do not admit that we are
within the category of persons whose consent is required under Section 7 of the
Securities Act or the rules and regulations of the Securities and Exchange
Commission issued thereunder.

                                          Very truly yours,

                                          /s/ VINSON & ELKINS L.L.P.

                                          Vinson & Elkins L.L.P.