SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                    FORM 8-K

                                 Current Report
                     Pursuant to Section 13 or 15(d) of the
                         Securities Exchange Act of 1934

                                  May 21, 2004
                Date of Report (Date of earliest event reported)

                        Endurance Specialty Holdings Ltd.
              Exact name of registrant as specified in its charter)

           Bermuda                    1-31599                    98-032908
(State or Other Jurisdiction  (Commission File Number)       (I.R.S. Employer
     of Incorporation)                                      Identification No.)

           Wellesley House, 90 Pitts Bay Road, Pembroke HM 08, Bermuda
          (Address of principal executive offices, including zip code)

                                 (441) 278-0440
              (Reigstrant's telephone number, including area code)

                                 Not Applicable
          (Former name or former address, if changed since last report)



Item 5. Other Events

      On May 24, 2004, Endurance Specialty Holdings Ltd. (the "Company")
announced that its Board of Directors authorized the Company to engage in two
capital management initiatives: (i) the repurchase of 2,036,834 of its ordinary
shares owned by Lightyear Capital, an initial investor at the Company's
formation, at a purchase price of $31.779 per share; and (ii) the initiation of
a share repurchase program by the Company for the repurchase of up to 2,000,000
ordinary shares and ordinary share equivalents in open market or privately
negotiated transactions, from time to time, depending on market conditions. The
share repurchase program is currently authorized to continue until May 2006.

      On May 24, 2004, the Company issued a press release announcing these
capital management initiatives. The press release is attached hereto as Exhibit
99.2 and is incorporated herein by reference.



                                    SIGNATURE

      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.

Dated: May 25, 2004

                                            By: /s/ John V. Del Col
                                               --------------------------------
                                            Name: John V. Del Col
                                            Title: General Counsel & Secretary



                                  EXHIBIT INDEX

Exhibit No.          Description
- -----------          -----------

       99.1          Share Purchase Agreement, dated as of May 21, 2004, between
                     LY-Endurance, LLC and Endurance Specialty Holdings Ltd.

       99.2          Press Release of Endurance Specialty Holdings Ltd., dated
                     May 24, 2004