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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 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





                           Converium Holding Ltd, Zug

Zug, Switzerland - August 20, 2004 - Converium to inform on external
reserve review and resulting capital measures on August 31, 2004

On July 27, 2004 Converium announced the appointment of a leading firm of
consulting actuaries to conduct an external actuarial study of the Company's
reserves held in respect of the Zurich and New York businesses. It was also
stated that this review would be completed before the end of August, specific
information on measures to restore the Company's strong capitalization being
communicated thereafter.

This is to inform that Converium is on track as regards these efforts. The
Company will issue a detailed announcement on Tuesday, August 31, 2004 and hold
an analyst and media conference call the same day at 3 p.m. CET to discuss the
outcome of the reserve review and resulting capital measures. This call will be
simultaneously webcast and can be accessed through Converium's website at
www.converium.com. Dial-in details will be provided in the press release.



Enquiries:

Michael Schiendorfer                      Zuzana Drozd
Media Relations Manager                   Head of Investor Relations

michael.schiendorfer@converium.com        zuzana.drozd@converium.com

Phone:        +41 (0) 1 639 96 57         Phone:  +41 (0) 1 639 91 20
Fax:          +41 (0) 1 639 76 57         Fax:    +41 (0) 1 639 71 20


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:     General Legal Counsel



Date:  August 20, 2004