EXHIBIT 5.1

                           FULBRIGHT & JAWORSKI L.L.P.
                            1301 McKinney, Suite 5100
                              Houston, Texas 77010

June 21, 2004

EOG Resources, Inc.
333 Clay Street, Suite 4200
Houston, Texas 77002

Ladies and Gentlemen:

      We have acted as counsel for EOG Resources, Inc., a Delaware corporation
(the "Registrant"), in connection with the registration under the Securities Act
of 1933 of an aggregate of 4,000,000 shares of the Registrant's common stock,
par value $.01 per share (the "Shares"), which are to be offered upon the terms
and subject to the conditions set forth in the Amended and Restated EOG
Resources, Inc. 1992 Stock Plan (the "Stock Plan"). The Shares may consist of
(i) the Registrant's authorized but unissued shares of common stock (the
"Original Issuance Shares"), (ii) previously issued shares of the Registrant's
common stock reacquired and held by the Registrant or (iii) shares of the
Registrant's common stock purchased on the open market.

      In connection therewith, we have examined originals or copies, certified
or otherwise identified to our satisfaction, of the Certificate of Incorporation
of the Registrant, the Bylaws of the Registrant, the Stock Plan, the records of
relevant corporate proceedings and such other documents and instruments as we
have deemed necessary or appropriate for the expression of the opinions
contained herein. We also have examined the Registrant's Registration Statement
on Form S-8 (the "Registration Statement") to be filed with the Securities and
Exchange commission with respect to the Shares.

      We have assumed the authenticity and completeness of all records,
certificates and other instruments submitted to us as originals, the conformity
to original documents of all records, certificates and other instruments
submitted to us as copies, the authenticity and completeness of the originals of
those records, certificates and other instruments submitted to us as copies and
the correctness of all statements of fact contained in all records, certificates
and other instruments that we have examined.

      Based on the foregoing, and having regard for such legal considerations as
we have deemed relevant, we are of the opinion that upon the issuance and sale
of the Original Issuance

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Shares pursuant to the provisions of the Stock Plan, such Original Issuance
Shares will be duly authorized and validly issued, fully paid and nonassessable.

      We hereby consent to the filing of this opinion as an exhibit to the
Registration Statement and to the reference to our name under the caption "Item
5. Interests of Named Experts and Counsel" in the Registration Statement.

                                           Very truly yours,

                                           /s/ FULBRIGHT & JAWORSKI  L.L.P.

                                           Fulbright & Jaworski L.L.P.

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