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 Quarterly Report on Form 10-Q for the quarterly period ended June
         30, 2005 (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:  August 4, 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 Quarterly Report on Form 10-Q for the quarterly period ended June
         30, 2005 (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:  August 4, 2005

                                            /s/ TERRY G. DALLAS
                                           ----------------------------
                                            Terry G. Dallas