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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



                                   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 27, 2004



                           Converium Holding Ltd, Zug


Zug, Switzerland - September 23, 2004 - Converium informs on the Extraordinary
General Meeting (EGM) to be held on September 28, 2004


Converium considering a range of strategic options
Following a careful examination of the Company's track record and franchise
outside the United States, the Board of Directors of Converium believes that the
Company has a viable business future as a professional reinsurer. In this
context, Converium is considering a range of strategic options, which include a
capital increase, a partnership, a strategic investment, or a combination
thereof.

Non-US franchise historically a strong source of earnings
Converium has a track record of building profitable businesses in key markets
such as Europe, Asia-Pacific and Latin America. Since Converium's Initial Public
Offering (IPO) the Company has generated net income in excess of US$ 500 million
excluding business underwritten by the North American entity. The Company
believes that despite the set backs suffered in the United States, it continues
to enjoy a strong and stable franchise among its customers in the remaining
markets. An independent survey from Flashpoehler conducted in the first half of
2004 among European cedents indicates that Converium's clients rank the Company
3rd in terms of overall excellence among all reinsurers surveyed. Against this
backdrop Converium's Board of Directors believes that the Company can continue
to extract value from this franchise for the benefit of shareholders. As a
consequence, a going concern on a stand-alone basis based on a capital increase
remains a viable option.


Converium is committed to maintain maximum flexibility as regards strategic
options
In considering all options to protect the Company's franchise and shareholders'
value, flexibility is an essential component of this process. A capital increase
is a core ingredient in a number of these options. Converium is currently
discussing a partnership or strategic investment with various parties. While
some discussions are at a more advanced stage, additional time will be needed in
order to diligently evaluate and compare all options when it comes to structures
and terms. The progress of a number of discussions is dependent on assurances to
the potential partners that the capital increase will be available.

Converium's Board of Directors stresses that the Company will only execute a
capital increase that makes sense from a shareholder value and rating
perspective and on underwriting terms that are acceptable to the Company.

The Board of Directors is proposing a flexible capital increase structure to the
EGM
Against this backdrop, the Board of Directors proposes that shareholders approve
a capital structure allowing a capital increase of up to $420 million for

     o    a discounted rights issue for existing shareholders and, if
          appropriate,

     o    a tranche for a strategic investment or partnership for which
          pre-emptive rights are excluded.



Board of Directors seeks shareholder approval of the proposed capital increase
While the Board of Directors appreciates that several questions may remain
outstanding, having the capital increase approved will give the Company the
necessary flexibility to effectively evaluate all options. Not having approval
will restrain Converium's strategic and tactical flexibility and may ultimately
force the Company to consider alternatives which may not result in achieving an
outcome that generates the best value for shareholders.


                                  * * * * * * *


Converence call details

Converium will hold a conference call for the investment community and is
pleased to invite you to participate. This call will be webcast live on the
internet at www.converium.com. Please dial in 10 - 15 minutes before and ensure
that you have Real Media Player or Windows Media Player.

The conference call will be held on Thursday, September 23, 2004
at     10:00 a.m. Central European Time (CET)
       09:00 a.m. Greenwich Mean Time (GMT)
       04:00 a.m. Eastern Standard Time (EST)
       01:00 a.m. Pacific Standard Time (PST)

call   +41 (0) 91 610 5600 (Europe)
       +44 (0) 207 107 0611 (UK)
       +1 (1) 866 291 4166 (Toll Free USA only)
       +1 866 519 5086 (Toll Free Canada)
       +1 866 519 5087 (Toll Free Mexico)

and quote "Converium"

For those of you unable to participate actively in this conference call, an
audio recording will be available one hour after the event for 24 hours. The
number to dial and the access code are as follows:

       +44 (0) 207 866 4300 from UK
       +41 (0) 91 612 4330 from Europe
       +1 412 317 0088 from North America

followed by the access code 196 #

A few hours after the event the full webcast with Q&A is for the period of one
month available on www.converium.com.



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 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.

This document does not constitute or form part of an offer or solicitation of an
offer, an invitation to subscribe for or purchase any securities. In addition,
the securities of the company to be issued in any share offering have not and
will not be registered under the United States securities laws and may not be
offered, sold or delivered within the United States or to US persons absent
registration under or an exemption from the registration requirements of the
United States securities laws.


www.converium.com
-----------------