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 March 31,
     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:  May 5, 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 March 31,
     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:  May 5, 2005

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