Murphy Oil (MUR) 10-Q 2004 Q3 Quarterly report

EXHIBIT 32

CERTIFICATION 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 Murphy Oil Corporation (the “Company”) on Form 10-Q for the period ended September 30, 2004 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), we, Claiborne P. Deming and Steven A. Cossé, Principal Executive Officer and Principal Financial Officer, respectively, of the Company, certify, pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, that to our knowledge:

(1) The Report fully complies with the requirements of section 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.

November 5, 2004

/s/ Claiborne P. Deming

Claiborne P. Deming

Principal Executive Officer

/s/ Steven A. Cossé

Steven A. Cossé

Principal Financial Officer

Ex. 32-1