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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 September, 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






                           Converium Holding Ltd, Zug

Zug, Switzerland - September 10, 2004 - Converium comments on Standard &
Poor's rating decision and announces the placing into run-off of its US
operations


Converium to consider changes to its global business plan
Converium is disappointed with Standard & Poor's decision to lower the
Company's ratings to BBB from A-. Converium, however, will make all efforts to
maintain its franchise. Today's rating action by Standard & Poor's, in
conjunction with A.M. Best's recent downgrading of Converium, has required
changes to the Company's global business plan which will be communicated
shortly. As a consequence of the rating action taken by Standard & Poor's,
Converium is reviewing all options with its banks concerning the proposed share
issue announced on September 3, 2004.

Converium to place its US operations into run-off
In the wake of A.M. Best's recent downgrading of Converium to B++ the
Company will not inject any additional capital into Converium Insurance (North
America) Inc. (CINA) as originally planned. The proceeds from Converium's
proposed capital raising will be used to strengthen the capitalization of
Converium AG, Zurich, and Converium Ruckversicherung AG (Deutschland), Cologne,
in order to protect the Company's franchise outside the US. The Company will
therefore place its US operations into run-off, i.e. no longer write reinsurance
from the US. Converium intends, however, to continue underwriting US exposure
from Converium AG, Zurich, and its Bermuda Branch. In this context, Converium is
currently discussing fronting arrangements with third parties for the existing
Global Aerospace Underwriting Managers Ltd. (GAUM) business written by CINA.
Converium is committed to ensure an orderly run-off of the reserves that the
Company carries in its North American legal entities and will continue to
negotiate commutations and to conduct claims and underwriting audits.

Resignation of Gary Prestia
As a result of these developments Gary Prestia, member of Converium's
Global Executive Committee and Chief Technical Officer, has submitted his
resignation as president of Converium Reinsurance (North America) Inc. (CRNA).
Converium regrets his decision to leave the Company and thanks Mr. Prestia for
his valuable contribution to the Company. His successor will be Corcoran Byrne,
currently General Counsel of CRNA.

                                  * * * * * * *

Enquiries:

Dr Kai-Uwe Schanz                         Zuzana Drozd
Chief Communication Officer               Head of Investor Relations
kai-uwe.schanz@converium.com              zuzana.drozd@converium.com
Phone:   +41 (0) 1 639 90 35              Phone:    +41 (0) 1 639 91 20
Fax:     +41 (0) 1 639 70 35              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 a "BBB"
rating (watch developing) from Standard & Poor's and a "B++" (outlook negative)
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







                                   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:  September 16, 2004