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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

Zug, Switzerland - July 20, 2004 - Converium deals with pre-IPO legacy issues in
US Casualty business.

     o    Converium's second quarter results to be impacted by a reserve
          strengthening for US casualty business and subsequent asset
          impairments on the balance sheet of Converium Reinsurance (North
          America) Inc.
     o    Pre-IPO legacy issues being dealt with
     o    Converium explores all options for maintaining strong capitalization
     o    Second quarter results and further information to be provided on July
          27, 2004

Converium's second quarter results will fall short of expectations due to higher
than modeled US casualty loss emergence primarily related to the underwriting
years 1997 to 2001. Reserves for these lines of business, in particular
umbrella, professional liability and Excess & Surplus Lines casualty, will be
bolstered by up to US$ 400 million. This reserve action triggers net impairments
of up to US$ 289 million of Deferred Tax Assets and US$ 94 million of Goodwill
in the balance sheet of Converium Reinsurance (North America) Inc.

On April 29, 2004 Converium announced that first quarter reported losses from
prior year US casualty business had exceeded expected loss emergence. In the
same press release, Converium also stated the expectation that the volatility of
longer-tail risks was likely to persist for some time. This adverse loss
reporting trend has continued and accelerated in the second quarter of 2004.
Converium's decision to increase reserves at this time should be seen in the
context of an ongoing reserve strengthening for prior years at US primary
insurance companies, triggered, in part, by the increased pressure for enhanced
disclosure.

In response to the loss developments observed in the last quarters, Converium
has initiated additional reviews of the US casualty business in order to examine
the adequacy of prior years' provisions from an integrated actuarial,
underwriting and claims perspective. At this point in time these ongoing
internal reviews indicate a potential overall reserve shortfall relating to
Converium's US casualty business of up to US$ 400 million. In addition,
Converium has commissioned a leading firm of consulting actuaries to conduct a
comprehensive and detailed external review. The outcome of their analysis will
be communicated before the end of August.

Dirk Lohmann, CEO, said: "I am personally leading this comprehensive review with
the assistance of our actuarial team and members of the newly created
Underwriting Technical Services team under Gary Prestia's leadership. Let me
stress that I am absolutely determined to put an end to this US casualty
reserving saga."

The CEO added: "Although the latest set of reserve increases is a disappointment
for all stakeholders, our ongoing business is performing well and our franchise
in the global reinsurance markets remains strong. We have a new and better
business model and a strengthened management team. The problems of the past have
been isolated and are being addressed. With the impairment of the Deferred Tax
Asset and the Goodwill on the North American balance sheet, the last of the
legacy issues from the old Zurich Re have been eliminated. Over the next few
weeks we will explore all options for maintaining Converium's strong
capitalization, including the raising of additional capital, in order to meet
the objectives of our shareholders, clients, intermediaries and other
stakeholders."





Martin Kauer, CFO, said: "The rating agencies and most investment analysts do
not fully consider soft assets such as Deferred Tax Assets and Goodwill when
evaluating the value of a company. They focus on the net tangible book value,
which excludes these two balance sheet items. From an economic perspective the
North American Deferred Tax Asset will no longer be on Converium's consolidated
balance sheet; from a tax perspective, however, we may be able to offset any
future profits against these tax losses, thus reducing significantly our future
tax rate."

Further information will be provided on July 27, 2004 as part of Converium's
quarterly reporting.

An Analyst and Media Conference Call will take place on Tuesday, July 20, 2004
from 12:00 to 13:00 p.m. CET, please call +41 (0) 91 610 5600 (Europe), +1 (1)
866 291 4166 (Toll Free USA only), +44 (0) 207 107 0611 (UK), +1 866 519 5086
(Toll Free Canada), +1 866 519 5087 (Toll Free Mexico) and quote "Converium".

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 perspectives on its value drivers, its strategic
initiatives and those factors critical to understanding its business and
operating environment.



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 (stable 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.

This document does not constitute, or form a part of, an offer, or solicitation
of an offer, or invitation to subscribe for or purchase any securities of the
Company.

www.converium.com