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 April, 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 - April 11, 2006 - Converium informs about today's Annual
General Meeting, the following constituent meeting of the Board of Directors and
the election of Markus Dennler as new Chairman.

At today's Annual General Meeting of Converium Holding Ltd, 185 shareholders
representing 42,515,778 registered shares or 28.98% of outstanding share capital
were present or represented.

The shareholders have taken the following decisions:

Agenda item 1

Approval of the annual report, the annual financial statements and consolidated
statements for 2005, as well as acknowledgment of the auditor's and group
auditors' reports by 99.42% affirmative votes.

Agenda item 2

The General Meeting has approved by 99.81% affirmative votes to allocate the
available earnings of the financial year 2005 as follows:

Net income for the financial year 2005                     CHF       26,191,677
Retained earnings brought forward from the previous year   CHF                -
Available earnings                                         CHF       26,191,677
                                                           --------------------
Allocation to general legal reserve (Art. 671 CO)          CHF                -
Allocation to dividends                                    CHF       14,668,946
                                                           --------------------
Retained earnings carried forward                          CHF       11,522,731

The total allocation to dividends of CHF 14,668,946 will result in a gross
dividend of CHF 0.10 per registered share entitled to dividends. The dividend
payment will be made as from April 18, 2006.

Agenda item 3

The General Meeting has approved the release of the members of the Board of
Directors and of the management from liability for their business activities for
the year 2005 by 98.57% affirmative votes.

Agenda item 4

The General Meeting has elected the following persons to the Board of Directors
for a term of office of three years:




Mr Lennart Blecher - 98.62% affirmative votes.
Mr Detlev Bremkamp - 94.68% affirmative votes.
Mr Harald Wiedmann - 88.54% affirmative votes.

Agenda item 5.1

The General Meeting approved by 99.68% affirmative votes the extension of the
two-year term, until April 11, 2008, for the Board of Directors to increase the
share capital by the issue of up to a maximum of 4,000,000 fully paid-up
registered shares each of CHF 5.00 nominal value amounting to a maximum of CHF
20,000,000, and to amend Article 3b, paragraph 1 of the Articles of
Incorporation accordingly.

Agenda item 5.2

The following amendments to Article 5 of the Articles of Incorporation have been
approved by 97.17% affirmative votes:

Paragraph 1:
Unchanged

Paragraph 2:
Upon request, acquirers of shares are registered in the share register as
shareholders with the right to vote provided they declare explicitly to have
acquired the shares in their own name and for their own account.

Paragraph 3:
Persons not explicitly declaring themselves to be holding the shares in their
own name and for their own account ("nominees") are registered in the share
register as shareholders with voting rights without further inquiry up to a
maximum of 5%. (...)


Agenda item 6

The General Meeting has re-elected PricewaterhouseCoopers Ltd as auditors and
group auditors for a further term of one year by 99.71% affirmative votes.
Constituent meeting of the Board of Directors

In the constituent meeting of the Board of Directors, which took place after
today's Annual General Meeting, the composition of the different committees was
defined as follows:





Board of Directors
Chairman                                                Markus Dennler
Vice Chairman                                           Rudolf Kellenberger

Nomination and Remuneration Committee
Chairman                                                Detlev Bremkamp
Vice Chairman                                           Harald Wiedmann
Members                                                 Lennart Blecher
                                                        Markus Dennler

Finance and Risk Committee
Chairman                                                Lennart Blecher
Vice Chairman                                           Detlev Bremkamp
Members                                                 Derrell  Hendrix
                                                        Rudolf Kellenberger

Audit Committee
Chairman                                                Harald Wiedmann
Vice Chairman                                           Rudolf Kellenberger
Members                                                 Lennart Blecher
                                                        Markus Dennler

Markus Dennler, newly elected Chairman of the Board of Directors, stated: "I
feel honored and obliged by the trust placed in me. My colleagues and I will
build on Converium's successful stabilization in order to achieve a full
rebound. It remains our long-term objective to re-establish Converium as one of
the world's top ten reinsurance companies."

                                  * * * * * * *

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 US 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, certain
financial guidance such as the corporate tax rate, the reduction of CRNA net
liabilities , administration expense ratio and Corporate Center costs, the
rating environment, 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 US
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: April 12, 2006