Exhibit 32.1

I, Dirk Lohmann, Chief Executive Officer of Converium Holding AG, (the “Company”), certify, pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, 18 U.S.C. Section 1350, that to the best of my knowledge:

(1) the Annual Report on Form 20-F of the Company for the fiscal year ended December 31, 2003 (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, the financial condition and results of operations of the Company.

Date: April 5, 2004

By:	/s/ Dirk Lohmann
Dirk Lohmann
Chief Executive Officer, Converium Holding AG