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, 2005

                              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




Repurchase of shares for Employee Participation Plans

Zug,  Switzerland - July 4, 2005 - Converium Holding AG has repurchased  200'000
shares in the period of April 1 through June 30, 2005 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.

Contacts:

Zuzana Drozd
Head of Investor Relations
zuzana.drozd@converium.com
Phone    +41 (0) 44 639 91 20
Fax      +41 (0) 44 639 71 20


Esther Gerster
Head of Public Relations
esther.gerster@converium.com
Phone    +41 (0) 44 639 90 22
Fax      +41 (0) 44 639 70 22



www.converium.com



                                   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/ Terry Clarke
                                             ----------------
                                             Name:      Terry Clarke
                                             Title:     CEO


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



Date: July 4, 2005