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                                    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 July, 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






Converium Holding AG: Repurchase of shares for Employee Participation Plans


Converium Holding AG has repurchased 50'000 shares in the period of April 1
through June 30, 2004 on the SWX Swiss Exchange in conjunction with its share
delivery obligations under the various Employee Participation Plans.

Converium Holding AG will continue its repurchases of own stock in order to
fulfil its share delivery obligations under the various Employee Participation
Plans.




                                   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: July 9, 2004