EXHIBIT 4.1


               AMENDMENT NO. 6 TO RIGHTS AGREEMENT


          AMENDMENT NO. 6 (this "Amendment No. 6"), dated as of
June 15, 2005, to the Rights Agreement, dated as of February 14,
2000, as amended, by and between EOG Resources, Inc. (the
"Company") and EquiServe Trust Company, N.A. (as Rights Agent)
(the "Rights Agreement").  Terms used herein but not defined
shall have the meanings assigned to them in the Rights Agreement.

          WHEREAS, the Company and the Rights Agent have
heretofore executed and entered into the Rights Agreement; and

          WHEREAS, pursuant to Section 27 of the Rights
Agreement, the Company may from time to time supplement or amend
the Rights Agreement in accordance with the provisions of such
Section 27; and

          WHEREAS, the Board of Directors of the Company has
determined that it is in the best interest of the Company and its
stockholders to amend the Rights Agreement to provide that any
"Person" that is a "Qualified Institutional Investor" (as defined
herein) will not be deemed an "Acquiring Person" (as defined in
the Rights Agreement).

          NOW, THEREFORE, the Company and the Rights Agent hereby
amend the Rights Agreement as follows:

          The definition of "Qualified Institutional Investor"
that appears in Section 1 of the Rights Agreement is hereby
amended to read in its entirety as follows:

     "Qualified Institutional Investor" shall mean, as of any
     time of determination, a Person that is described in Rule
     13d-l(b)(1) promulgated under the Exchange Act (as such Rule
     is in effect on the date hereof) and is eligible to report
     (and, if such Person is the Beneficial Owner of greater than
     5% of the Common Shares of the Company, does in fact report)
     beneficial ownership of Common Shares of the Company on
     Schedule 13G, and such Person (i) is not required to file a
     Schedule 13D (or any successor or comparable report) with
     respect to its beneficial ownership of Common Shares of the
     Company, and (ii) shall be the Beneficial Owner of less than
     15% of the Common Shares of the Company then outstanding;
     provided, however, that a Person which would constitute a
     Qualified Institutional Investor except for its failure to
     satisfy clause (ii) of this definition shall nonetheless
     constitute a Qualified Institutional Investor if (A) such
     Person or an Affiliate of such Person shall have, as of
     December 31, 2004, reported beneficial ownership of greater
     than 5% of the Common Shares of the Company for a period of
     two consecutive years and shall thereafter continuously
     beneficially own greater than 5% of the Common Shares of the
     Company then outstanding prior to the time of determination,
     (B) such Person shall be the Beneficial Owner of less than
     15% of the Common Shares of the Company then outstanding
     (including in such calculation the holdings of all of such
     Person's Affiliates and Associates other than those which,
     under published interpretations of the SEC or its Staff, are
     eligible to file separate reports on Schedule 13G with
     respect to their beneficial ownership of the Common Shares
     of the Company), and (C) such Person shall be the Beneficial
     Owner of less than 30% of the Common Shares of the Company
     then outstanding."

          Section 18 of the Rights Agreement is hereby amended by
adding the following paragraph to the end of such section:

     "Notwithstanding anything to the contrary contained herein,
     Rights Agent shall not be liable for any delays or failures
     in performance resulting from acts beyond its reasonable
     control, including, without limitation, acts of God,
     terrorist acts, shortage of supply, breakdowns or
     malfunctions, power failures or mechanical difficulties with
     information storage or retrieval systems, labor
     difficulties, war, or civil unrest."

          Section 21 of the Rights Agreement is hereby amended by
adding the following after the first sentence thereof:

     "In the event the transfer agency relationship in effect
     between the Company and the Rights Agent is terminated by
     the Company, the Rights Agent will be deemed to resign
     automatically on the effective date of such termination, and
     any notice required under the immediately preceding sentence
     will be sent by the Company rather than the Rights Agent."

          IN WITNESS WHEREOF, this Amendment No. 6 has been duly
executed by the Company and the Rights Agent as of the day and
year first written above.

                              EOG RESOURCES, INC.


                              By: /s/ PATRICIA EDWARDS
                                  Name:  Patricia Edwards
                                  Title: Vice President, Human Resources,
                                          Administration & Corporate Secrtary


                              EQUISERVE TRUST COMPANY, N.A.
                              (as Rights Agent)


                              By: /s/ KEVIN LAURITA
                                  Name:  Kevin Laurita
                                  Title: Managing Director