Hess (HES) 10-Q 2004 Q2 Quarterly report

Exhibit 32(1)

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 Amerada Hess Corporation (the “Corporation”) on Form 10-Q for the period ending June 30, 2004 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, John B. Hess, Chairman of the Board and Chief Executive Officer of the Corporation, certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

(1)	The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and
(2)	The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Corporation.

	By /s/ John B. Hess
	JOHN B. HESS
Date: August 6, 2004	CHAIRMAN OF THE BOARD AND CHIEF EXECUTIVE OFFICER

A signed original of this written statement required by Section 906 has been provided to Amerada Hess Corporation and will be retained by Amerada Hess Corporation and furnished to the Securities and Exchange Commission or its staff upon request.

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