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, 2006

                              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

Zug, Switzerland - July 5, 2006 Converium Holding AG has repurchased 100'000
shares in the period of April 1 through June 30, 2006 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





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/ Inga Beale
                                      Name:      Inga Beale
                                      Title:     CEO




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



Date: July 5, 2006