Exhibit 32.1

CERTIFICATION OF
CHIEF EXECUTIVE OFFICER
OF CLAYTON WILLIAMS ENERGY, INC.
PURSUANT TO 18 U.S.C. §1350

In connection with the accompanying report on Form 10-Q/A for the period ended March 31, 2004 and filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Clayton W. Williams, Chief Executive Officer of Clayton Williams Energy, Inc. (the “Company”), hereby certify 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/Clayton W. Williams

Clayton W. Williams

Chief Executive Officer

October 14, 2004