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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 July, 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:  July 21, 2004





                           Converium Holding Ltd, Zug

Converium notes the uncertainty regarding the impact of today's announcement
regarding its insurance reserves on the 8.25% guaranteed Subordinated Notes due
2032 issued by Converium Finance S.A. and guaranteed by Converium Holding A.G.
and Converium A.G.

The strengthening of reserves and related asset impairments announced today
should not impact Converium's ability to service the notes. As of March 31,
2004, Converium had total assets of more than US$15 billion, cash and cash
equivalents of more than US$300 million and shareholders' equity of US$2.2
billion. Converium will announce its results for the second quarter of 2004 on
July 27, 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


About Converium

Converium is an independent leading global multi-line reinsurer known for its
innovation, professionalism and service. Today Converium ranks among the top ten
professional reinsurers and employs approximately 850 people in 23 offices
around the globe. Converium is organized into three business segments: Standard
Property & Casualty Reinsurance, Specialty Lines and Life & Health Reinsurance.
Converium's net losses for the September 11, 2001 terrorist attacks in the
United States are capped at US$ 289.2 million by its former parent, Zurich
Financial Services. Converium has minimal A&E exposures. Converium has an "-A"
rating (negative outlook) both from Standard & Poor's and A.M. Best Company.

Important Disclaimer

This document contains forward-looking statements as defined in the U.S. Private
Securities Litigation Reform Act of 1995. It contains forward-looking statements
and information relating to the Company's financial condition, results of
operations, business, strategy and plans, based on currently available
information. These statements are often, but not always, made through the use of
words or phrases such as `expects', `should continue', `believes',
`anticipates', `estimates' and `intends'. The specific forward-looking
statements cover, among other matters, our reserve position, the elimination of
legacy issues from Zurich Re, loss reporting trends and our business plans. Such
statements are inherently subject to certain risks and uncertainties. Actual
future results and trends could differ materially from those set forth in such
statements due to various factors. Such factors include general economic
conditions, including in particular economic conditions; the frequency, severity
and development of insured loss events arising out of catastrophes, as well as
man-made disasters such as the September 11, 2001 attack on the United States;
the ability to exclude and to reinsure the risk of loss from terrorism;
fluctuations in interest rates; returns on and fluctuations in the value of
fixed income investments, equity investments and properties; fluctuations in
foreign currency exchange rates; rating agency actions; changes in laws and
regulations and general competitive factors, and other risks and uncertainties,
including those detailed in the Company's filings with the U.S. Securities and
Exchange Commission and the SWX Swiss Exchange. The Company does not assume any
obligation to update any forward-looking statements, whether as a result of new
information, future events or otherwise.


www.converium.com