OMB APPROVAL

                                                           OMB Number: 3235-0116

                                                        Expires: March 31, 2003

                                                        Estimated average burden
                                                        hours per response: 8



                                    Form 6-K

                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                        Report of Foreign Private Issuer

                        Pursuant to Rule 13a-16 or 15d-16
                     of the Securities Exchange Act of 1934

                           For the month of May, 2004

                              CONVERIUM HOLDING AG
                   ------------------------------------------
                 (Translation of registrant's name into English)

                                 Baarerstrasse 8
                                   CH-6300 Zug
                                   Switzerland
             -------------------------------------------------------
                    (Address of principal executive offices)

Indicate by check mark whether the registrant files or will file annual reports
under cover Form 20-F or Form 40-F.

                        Form 20-F  __X__   Form 40-F _____


Indicate by check mark whether the registrant by furnishing the information
contained in this Form is also thereby furnishing the information to the
Commission pursuant to Rule 12g3-2(b) under the Securities Exchange Act of 1934.

                              Yes  ______         No __X___


If "Yes" is marked,  indicate  the file  number  assigned to the  registrant  in
connection with Rule 12g3-2(b): 82- Not Applicable






990231.3





                                         SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned, thereunto duly authorized.


                                        CONVERIUM HOLDING AG




                                        By:  /s/ Dirk Lohmann
                                             Name:    Dirk Lohmann
                                             Title:   CEO




                                        By:  /s/ Christian Felderer
                                             Name:    Christian Felderer
                                             Title:   General Legal Counsel



Date:  May 5, 2004






Disclosures with respect to Converium Holding Ltd's 4th Annual General Meeting

Issuer:            Converium Holding Ltd
Sec. ID no.:       1'299'771
ISIN:              CH0012997711



In accordance with art. 8 of the Articles of Incorporation of Converium Holding
Ltd and with para. 3.01 (date of the next shareholders' meeting) of the revised
checklist [with effect from February 1, 2004] published as enclosure 1 of the
"Reports required in order to maintain a listing" (Art. 64 - 75 KR), we herewith
inform you that the next ordinary shareholders' meeting of Converium Holding Ltd
will take place April 12, 2005 at 10.30 hours in the Theater Casino, in Zug,
Switzerland.