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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 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







Dodge & Cox acquires 5.04% of Converium's registered shares
Disclosure of shareholdings pursuant to Art. 20 SESTA

Zug, Switzerland - June 22, 2005 - Converium Holding Ltd has been notified that
Dodge & Cox, 555 California Street, 40th Fl., San Francisco, CA 94104, U.S.A.,
has acquired 7,389,852 registered shares with voting rights. This corresponds to
5.04% of Converium's registered share capital. These shares are held and managed
in the Dodge & Cox International Stock Fund.

Dodge & Cox provides investment management to institutions and individuals
through separately managed portfolios and mutual funds.



Contacts:

Zuzana Drozd
Head of Investor Relations
zuzana.drozd@converium.com
Phone    +41 (0) 1 639 91 20
Fax      +41 (0) 1 639 71 20


Esther Gerster
Head of Public Relations
esther.gerster@converium.com
Phone    +41 (0) 1 639 90 22
Fax      +41 (0) 1 639 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 23, 2005