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 June, 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








Capital Group Companies Inc. reduces its holding of Converium's registered
shares to below 5%
Disclosure of shareholdings pursuant to Art. 20 SESTA

Zug, Switzerland - June 29, 2005 - Converium Holding Ltd has been notified that
Capital Group Companies Inc., 333 South Hope Street, Los Angeles, CA,
90071-1406, USA acting on behalf of funds managed by Capital Research and
Management Company, 333 South Hope Street, Los Angeles, CA, USA, and clients of
Capital Guardian Trust Company, 11100 Santa Monica Blvd 15th Floor, Los Angeles,
CA, USA, Capital International Ltd., 25 Bedford St., London, England, Capital
International Inc., 11100 Santa Monica Blvd 15th Floor, Los Angeles, CA, USA,
and Capital International S.A., 3 Place des Bergues, 1201 Geneva, Switzerland,
has reduced its holding of registered shares of Converium Holding Ltd, Zug to
below 5%.


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: June 29, 2005