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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, 2003

                              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






                                   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:    Group General Counsel



Date:  August 4, 2003