ConocoPhillips (COP) 10-Q 2003 Q3 Quarterly report

Exhibit 32

CERTIFICATIONS PURSUANT TO 18 U.S.C. SECTION 1350, AS ADOPTED
PURSUANT TO SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

     In connection with the Quarterly Report of ConocoPhillips (the company) on Form 10-Q for the period ending September 30, 2003, as filed with the U.S. Securities and Exchange Commission on the date hereof (the Report), each of the undersigned hereby certifies, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that to their knowledge:

(1) The Report fully complies with the requirements of Sections 13(a) or 15(d) 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 results of operations of the company.

Date:	Nov. 7, 2003
		J. J. Mulva
		J. J. Mulva President and Chief Executive Officer
		John A. Carrig
		John A. Carrig Executive Vice President, Finance, and Chief Financial Officer