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 Valero  Energy  Corporation  (the
Company) on Form 10-Q for the quarter  ending  September 30, 2003, as filed with
the  Securities  and Exchange  Commission  on the date hereof (the  Report),  I,
William E. Greehey,  Chief  Executive  Officer of the Company,  hereby  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; and

2.   The information  contained in the Report fairly  presents,  in all material
     respects, the financial condition and results of operations of the Company.



 /s/ William E. Greehey
- ----------------------------
William E. Greehey
Chief Executive Officer
November 14, 2003




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