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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 October, 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



                                   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:  October 8, 2004



Wellington Management Company LLC adjusts its holding in Converium shares to
below 5%

Converium Holding Ltd has been notified pursuant to Art. 20 of the Swiss Stock
Exchange Act that Wellington Management Company LLC, 75 State Street, Boston,
MA, 02100, USA, has adjusted its holding in Converium Holding Ltd, Zug to below
5% of Converium's registered shares.



Zug, October 5, 2004


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