EXHIBIT 32.1


                          CERTIFICATION WITH RESPECT TO
                               QUARTERLY REPORT OF
                          HCC INSURANCE HOLDINGS, INC.

         The undersigned, being the Chief Executive Officer and Chief Financial
Officer of HCC Insurance Holdings, Inc. (the "Company"), pursuant to 18 U.S.C.
ss. 1350 as adopted pursuant to ss.906 of the Sarbanes-Oxley Act of 2002, do
hereby certify to the best of their knowledge with respect to the Quarterly
Report of the Company on Form 10-Q, as filed with the Securities and Exchange
Commission for the quarter ended September 30, 2003, (the "Report"):

1.       that the Report fully complies with all requirements of section 13(a)
         and 15(d) of the Securities Exchange Act of 1934, as amended; and

2.       that the information contained in the Report fairly presents, in all
         material respects, the financial condition and results of operations of
         the Company.




 November 14, 2003                            /s/ Stephen L. Way
 -----------------               ----------------------------------------------
          (Date)                    Stephen L. Way, Chairman of the Board,
                                    Chief Executive Officer and President

 November 14, 2003                           /s/ Edward H. Ellis, Jr.
 -----------------               ----------------------------------------------
         (Date)                  Edward H. Ellis, Jr., Executive Vice President
                                         and Chief Financial Officer


A signed original of this written statement required by ss.906 has been provided
to HCC Insurance Holdings, Inc. and will be retained by HCC Insurance Holdings,
Inc. and furnished to the Securities and Exchange Commission or its staff upon
request.