Exhibit 32

CERTIFICATION OF CHIEF EXECUTIVE OFFICER

I, Charles R. Williamson, Chief Executive Officer of Unocal Corporation, certify, pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, 18 U.S.C. Section 1350, that, to my knowledge:

(1) our Annual Report on Form 10-K for the period ended December 31, 2004 (the “Report”), fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934 (15 U.S.C. 78m or 78o(d)); and

(2) the information contained in the Report fairly presents, in all material respects, our financial condition and results of operations.

Dated: March 8, 2005

/s/ CHARLES R. WILLIAMSON

Charles R. Williamson

CERTIFICATION OF CHIEF FINANCIAL OFFICER

I, Terry G. Dallas, Chief Financial Officer of Unocal Corporation, certify, pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, 18 U.S.C. Section 1350, that, to my knowledge:

(1) our Annual Report on Form 10-K for the period ended December 31, 2004 (the “Report”), fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934 (15 U.S.C. 78m or 78o(d)); and

(2) the information contained in the Report fairly presents, in all material respects, our financial condition and results of operations.

Dated: March 8, 2005

/s/ TERRY G. DALLAS

Terry G. Dallas