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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 May, 2006

                              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 - May 9, 2006 - Converium reports successful April 1 treaty
renewals with stable premium volume.

Converium recorded a successful April 1 renewal of non-life treaties. The
Company bound non-life contracts of US$ 272.2 million or 99.5% of the business
that was up for renewal. This result is fully in line with previously stated
expectations. It again testifies to the resilience of Converium's franchise,
following the gratifying results of the January 1 renewals.

The April 1 renewals primarily included business written in Asia Pacific, as
well as from the Medical Defence Union (MDU) in the United Kingdom, a provider
of medical malpractice insurance coverage with whom Converium entertains a
long-standing strategic alliance.

In addition, some smaller Latin American and US casualty portfolios were up for
renewal. Consistent with its underwriting strategy Converium chose not to renew
US casualty business. Not taking into account this US book of business, overall
premium volume from the April 1 renewal has increased by 3.7%.

Asia Pacific

In Asia Pacific, Converium bound non-life business of US$ 62.4 million, a minor
decrease of 1.6%. In the Japanese market, which accounts for two thirds of the
renewed Asia Pacific book of business, premium volume was reduced by 2.9%.
Converium, however, successfully maintained its strong position with the largest
Japanese clients. In South Korea and India, the Company's book of business grew
by 2.4% and 16.2%, respectively.

Given the trend of clients retaining more risk and the resulting lower overall
reinsurance market volume, particularly in Japan, the renewal results are very
satisfactory. They demonstrate the robust quality of Converium's long-term
client relationships and are clear evidence of the Company's strong position in
the Asian markets.

Medical Defence Union

Converium is also very satisfied with the renewal of its Medical Defence Union
(MDU) book of business, which grew by 3.0% to US$ 168.1 million.

Reiteration of overall premium target for 2006

Following the results of the April renewals, Converium reiterates its
expectation of writing gross premiums for the 2006 calendar year of US$ 1.8 -
1.9 billion, including Life & Health business. The Company also re-affirms its
commitment to adhere to strict profitability standards.

Inga Beale, Chief Executive Officer, said: "I am very pleased with the April 1
renewals. The strong results reflect the loyalty of many of our Asian clients,
based on Converium's long-standing relationships and highly regarded technical
expertise. We will continue to develop our presence in Asia, which is one of our
key markets for future growth."



Inga Beale continued: "The long-term business of MDU remains an important part
of our book of business. We are proud of our fruitful relationship with the MDU
and look forward to continue providing high-quality services to our strategic
alliance partner."



                                  * * * * * * *


Enquiries:

Esther Gerster                           Zuzana Drozd
Head of Public Relations                 Head of Investor Relations
esther.gerster@converium.com             zuzana.drozd@converium.com
Phone:         +41 (0) 44 639 90 22      Phone:         +41 (0) 44 639 91 20
Fax:           +41 (0) 44 639 70 22      Fax:           +41 (0) 44 639 71 20



About Converium

Converium is an independent international multi-line reinsurer known for its
innovation, professionalism and service. Today Converium employs about 600
people in 18 offices around the globe and is organized into four business
segments: Standard Property & Casualty Reinsurance, Specialty Lines and Life &
Health Reinsurance, which are based principally on ongoing global lines of
business, as well as the Run-Off segment, which primarily comprises the business
from Converium Reinsurance (North America) Inc., excluding the US originated
aviation business portfolio. Converium has a "BBB+" rating (outlook stable) from
Standard & Poor's and a "B++" rating (outlook stable) 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 ` seek to', `expects', `should continue', `believes',
`anticipates', `estimates' and `intends'. The specific forward-looking
statements cover, among other matters, the Company's internal review and related
restatement, the reinsurance market, the Company's operating results, the rating
environment and the prospect for improving results and expense reductions. 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 the impact of our
ratings downgrade or a further lowering or loss of one of our financial strength
ratings; the impact of the restatement on our ratings and client relationships;
uncertainties of assumptions used in our reserving process; risk associated with
implementing our business strategies and our capital improvement measures and
the run-off of our North American business; cyclicality of the reinsurance
industry; the occurrence of natural and man-made catastrophic events with a
frequency or severity exceeding our estimates; acts of terrorism and acts of
war; changes in economic conditions, including interest and currency rate
conditions that could affect our investment portfolio; actions of competitors,
including industry consolidation and development of competing financial
products; a decrease in the level of demand for our reinsurance or increased
competition in our industries or markets; a loss of our key employees or
executive officers without suitable replacements being recruited within a
suitable period of time; our ability to address material weaknesses we have
identified in our internal control environment; political risks in the countries
in which we operate or in which we reinsure risks; the passage of additional
legislation or the promulgation of new regulation in a jurisdiction in which we
or our clients operate or where our subsidiaries are organized; the effect on us
and the insurance industry as a result of the investigations being carried out
by the US Securities and Exchange Commission, New York's Attorney General and
other governmental authorities; changes in our investment results due to the
changed composition of our invested assets or changes in our investment policy;
failure of our retrocessional reinsurers to honor their obligations or changes
in the credit worthiness of our reinsurers; our failure to prevail in any
current or future arbitration or litigation; and extraordinary events affecting
our clients, such as bankruptcies and liquidations , 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




                                   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/ Inga Beale
                                         Name:      Inga Beale
                                         Title:     CEO




                                    By:  /s/ Christian Felderer
                                         Name:   Christian Felderer
                                         Title:  General Legal Counsel



Date: May 10, 2006