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 August, 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



Capital Group Companies Inc.  adjusts its holding in Converium shares from 4.05%
to 5.34% (held and managed in various funds)


Converium Holding Ltd has been notified that Capital Group Companies Inc., 333
South Hope Street, Los Angeles, CA, 90071-1406, USA, has increased as a group
its holding 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,
to 2,137,095 registered shares in Converium Holding Ltd, Zug. This corresponds
to 5.34% of Converium's registered shares. None of these entities represented by
Capital Group Companies Inc. individually holds shares of 5% or more of
Converium's registered share capital.

Zug, August 10, 2004

Contacts:



Zuzana Drozd
Head of Investor Relations
zuzana.drozd@converium.com

+41 (0)1 639 91 20


Michael Schiendorfer
Media Relations Manager
michael.Schiendorfer@converium.com
+41 (0)1 639 96 57
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/ Dirk Lohmann
                                           Name:      Dirk Lohmann
                                           Title:     CEO


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



Date:  August 13, 2004


Monthly disclosure of equity securities newly created from conditional capital