OMB APPROVAL
                                                        OMB Number: 3235-0116
                                                        Expires: March 31, 2003
                                                        Estimated average burden
                                                        hours per response: 8


                                    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, 2005

                              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 12, 2005 - Converium informs about today's Annual
General Meeting.

At today's Annual General Meeting of Converium Holding Ltd, 207 shareholders
representing 72'159'313 registered shares or 49.19% 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 and consolidated financial statements
for 2004, acknowledgment of the auditor's and group auditors' reports by 99.70%
affirmative votes.

Agenda item 2

In addition to the proposal in the invitation, the Board of Directors has
suggested not to carry forward the balance sheet loss of the financial year 2004
to the new account, but instead to allocate it to general reserve. The General
Meeting has approved this modified proposal of the Board by 99.80% affirmative
votes.

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 2004 by 66.27% 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:

Dr. Markus Dennler - 68.90% affirmative votes.

Mr Rudolf Kellenberger - 97.73% affirmative votes.





Agenda item 5

The General Meeting has re-elected PricewaterhouseCoopers Ltd as auditors and
group auditors for a further term of one year by 99.42% affirmative votes.

Peter Colombo,  Chairman of the Board of Directors,  stated: "The Board of
Directors is pleased with the support of its  proposals  by the  General
Meeting,  but  it has  also  acknowledged  the  critical  comments  by
individual shareholders.  Together  with the Global  Executive  Committee it
will do  everything  in its power to promote the turnaround of the company as
described by the CEO."

In the  constitutional  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:

Nomination Committee

Chairman          Dr. Markus Dennler
Vice Chairman     Prof. Dr. Anton K. Schnyder
Members           Peter Colombo
                  Rudolf Kellenberger

Remuneration Committee

Chairman          Georg Mehl
Vice Chairman     Prof. Dr. Anton K. Schnyder
Members           Peter Colombo
                  Rudolf Kellenberger

Finance Committee

Chairman          Prof. George Parker
Vice Chairman     Rudolf Kellenberger
Members           Dr. Markus Dennler
                  Georg Mehl

Audit Committee

Chairman          Peter Colombo
Vice Chairman     Prof. George Parker
Members           Dr. Markus Dennler
                  Georg Mehl

Terry G. Clarke and Derrell Hendrix will not be members of any committee.

                                  * * * * * * *



Enquiries:

Esther Gerster                                Zuzana Drozd
Head of Public Relations                      Head of Investor Relations
esther.gerster@converium.com                  zuzana.drozd@converium.com
Phone:         +41 (0) 1 639 90 22            Phone:         +41 (0) 1 639 91 20
Fax:           +41 (0) 1 639 70 22            Fax:           +41 (0) 1 639 71 20

About Converium

Converium is an independent  international  multi-line  reinsurer  known for its
innovation,  professionalism  and service.  Today  Converium  employs more than
700 people in 20 offices around the globe and is organized into three business
segments:  Standard  Property  & Casualty  Reinsurance,  Specialty  Lines and
Life & Health  Reinsurance. 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 reinsurance market, the Company's
operating results, the rating environment and the prospect for improving
results. 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 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. 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/ Terry Clarke
                                   Name:      Terry Clarke
                                   Title:     CEO




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



Date: April 14, 2005