Core Laboratories (CLB) 10-Q 2004 Q1 Quarterly report

Exhibit 32.1

Certification By

David M. Demshur, Chief Executive Officer

of Core Laboratories N.V.

Pursuant to 18 U.S.C. Sec 1350

I, David M. Demshur, Chief Executive Officer of Core Laboratories N.V. (the "Company"), hereby certify that the accompanying report on Form 10-Q for the quarter ended March 31, 2004, filed by the Company with the Securities and Exchange Commission on the date hereof pursuant to Section 13(a) of the Securities Exchange Act of 1934 (the "Report") fully complies with the requirements of that section.

I further certify that the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

	______/s/ David M. Demshur________
	Name: David M. Demshur
	Title: Chief Executive Officer
Date: May 7, 2004