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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 May, 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







990231.3







                                         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:  May 5, 2004






Monthly disclosure of equity securities newly created from conditional capital

Issuer:            Converium Holding AG
Sec. ID no.:       1'299'771
ISIN:              CH0012997711

In accordance with art. 3a of the Articles of Incorporation of Converium Holding
Ltd and with para. 5.02 (conditional capital) of the checklist published as
enclosure 1 of the "Reports required in order to maintain a listing" (Art. 64 -
75 KR), we inform about the creation of following share capital:

Newly created share capital

--  As at end of April 2004                    No new shares

--  As at end of previous month                6'217 Shares

Conditional capital                            No. of shares     CHF

--  Reserved for Employee Participation        4'000'000 Shares  CHF 40'000'000

--  Of which total exercised by end of
    April 2004                                 6'217 Shares      CHF     62'170

--  Remainder                                  3'993'783 Shares  CHF 39'937'830

Converium Holding Ltd's Annual General Meeting, held on April 27, 2004, approved
to  delete  art.  3a of  the  Articles  of  Incorporation.  Therefore  as of the
registration  of the  deletion of art.  3a in the  register  of  commerce,  this
disclosure will be dropped.