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

                                 October 4, 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
              (Registrant's telephone number, including area code)

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

Check the appropriate box below if the Form 8-K filing is intended to
simultaneously satisfy the filing obligation of the registrant under any of the
following provisions:

|_|   Written communications pursuant to Rule 425 under the Securities Act (17
       CFR 230.425)

|_|   Soliciting material pursuant to Rule 14a-12 under the Exchange Act (17 CFR
       240.14a-12)

|_|   Pre-commencement communications pursuant to Rule 14d-2(b) under the
       Exchange Act (17 CFR 240.14d-2(b))

|_|   Pre-commencement communications pursuant to Rule 13e-4(c) under the
       Exchange Act (17 CFR 240.13e-4(c))



Item 8.01. Other Events.

      On October 4, 2004, Endurance Specialty Holdings Ltd. issued the attached
press release, filed herewith as Exhibit 99.1 and incorporated herein by
reference.

Item 9.01. Financial Statements and Exhibits

      (c) Exhibits

      The following exhibits are filed as part of this report:

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

         99.1       Third Quarter Hurricanes Press Release, issued
                    October 4, 2004



                                   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.

Dated: October 4, 2004

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



                                  EXHIBIT INDEX

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

   99.1           Third Quarter Hurricanes Press Release, issued October 4, 2004