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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



                           Converium Holding Ltd, Zug


Zug, Switzerland, October 6, 2004: Converium has taken notice of information on
certain class action lawsuits which apparently were filed in the United States
District Court for the Southern District of New York on behalf of all securities
purchasers of Converium Holding AG ("Converium" or the "Company") from December
11, 2001 through July 20, 2004, inclusive (the "Class Period"). The Company has
not, thus far, been able to obtain the complaints from the court. Accordingly,
details of the specific nature of the claims and damages sought are not yet
available. The Company is not in a position to comment further at this stage.



                                  * * * * * * *

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 international multi-line reinsurer known for its
innovation, professionalism and service. Today Converium employs approximately
850 people in 23 offices around the globe and is organized into three business
segments: Standard Property & Casualty Reinsurance, Specialty Lines and Life &
Health Reinsurance. Converium Ltd has a "BBB" rating (watch positive) from
Standard & Poor's. Converium Holding Ltd has a "B++" (outlook stable) rating
from 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, the reinsurance market, the outcome of
insurance regulatory reviews, the Company's operating results, the rating
environment and the prospect for improving results, the amount of capital
required and impact of its capital improvement measures, including the
restructuring of our U.S. business and its reserve position. 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;
the outcome of our regular quarterly reserve review, our ability to raise
capital and the success of our capital improvement measures, the ability to
obtain applicable regulatory approval for our capital improvement measures, 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.



Please note that the company has made it a policy not to provide any quarterly
or annual earnings guidance and it will not update any past outlook for full
year earnings. It will however provide investors with perspective on its value
drivers, its strategic initiatives and those factors critical to understanding
its business and operating environment.

www.converium.com