Exhibit 32.1

Section 1350 Certification

     The undersigned, Bobby S. Shackouls, Chairman of the Board, President and Chief Executive Officer of Burlington Resources Inc. (“Company”), hereby certifies that the Quarterly Report of the Company on Form 10-Q for the period ended March 31, 2004 (the “Report”) (1) fully complies with the requirements of Section 13(a) of the Securities Exchange Act of 1934 and (2) the information contained in the Report fairly presents, in all material respects, the financial condition and the results of operations of the Company.

	/S/ BOBBY S. SHACKOULS
Dated: May 7, 2004	Bobby S. Shackouls
	Chairman of the Board, President and Chief Executive Officer

     This certification shall not be deemed to be “filed” for the purpose of Section 18 of the Securities Exchange Act of 1934, as amended, and will not be incorporated by reference into any registration statement filed under the Securities Act of 1933, as amended, unless specifically identified therein as being incorporated therein by reference.

     A signed original of this written statement required by Section 906, or other document authenticating, acknowledging, or otherwise adopting the signature that appears in typed form within the electronic version of this written statement required by Section 906, has been provided to Burlington Resources Inc. and will be retained by Burlington Resources Inc. and furnished to the Securities and Exchange Commission or its staff upon request.