UNITED STATES
                       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

                Date of Report (Date of earliest event reported)
                                November 2, 2004


                          HCC INSURANCE HOLDINGS, INC.
             (Exact name of registrant as specified in its charter)


           Delaware                   0-20766                76-0336636

 (State or other jurisdiction     (Commission File         (IRS Employer
      of incorporation)                Number)           Identification No.)

           13403 Northwest Freeway                  77040-6094
                Houston, Texas

    (Address of principal executive offices)         (Zip Code)

       Registrant's telephone number, including area code: (713) 690-7300


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 (see General Instruction A.2. below):

[ ] 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))

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Item 2.02. Results of Operations and Financial Condition.

     On November 2, 2004, HCC Insurance Holdings, Inc. announced its results for
the Third Quarter of 2004. A press release setting forth the announcement is
furnished as Exhibit 99.1 and is incorporated herein by reference.

Item 9.01 Financial Statements and Exhibits

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

   99.1             Earnings Press Release dated November 2, 2004

     The information contained herein shall not be deemed "filed" for purposes
of Section 18 of the Securities Exchange Act of 1934, as amended (the "Exchange
Act"), or otherwise subject to the liabilities of that section, nor shall it be
deemed incorporated by reference in any filing under the Securities Act of 1933,
as amended, or the Exchange Act.

                                   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 hereunto duly authorized.


                                                HCC INSURANCE HOLDINGS, INC.

Date: November 2, 2004
                                                By: /s/ CHRISTOPHER L. MARTIN
                                                    ----------------------------
                                                    Christopher L. Martin,
                                                    Executive Vice President and
                                                    General Counsel




                                  EXHIBIT INDEX
                                  -------------

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

   99.1             Earnings Press Release dated November 2, 2004