Exhibit 99.1

WALTER M. DUER JOINS HCC BOARD OF DIRECTORS

HOUSTON (July 12, 2004) . . .
HCC Insurance Holdings, Inc. (NYSE symbol: HCC) announced today that Walter M. Duer, CPA had agreed to join the Board of Directors of the Company, effective July 12, 2004.

Mr. Duer, who lives in Houston, recently retired as the National Managing Partner of KPMG’s Business Integration & Divestiture Practice. His 36 years career at KPMG has been largely in taxation and the insurance industry and he was a member of the firm’s Board of Directors, the Board’s Finance Subcommittee and a KPMG Foundation Trustee.

Mr. Duer has a degree in Business Administration from Wagner College and attended advance curriculum at Pace University. He is a member of the AICPA and the Texas Society of Certified Public Accountants. He is the author of “An Executives Guide to Alternative Insurance Markets and Programs” and is recognized as an expert on captive insurance companies.

Mr. Duer will also be a member of the Company’s Audit Committee.

Stephen L. Way, Chairman and Chief Executive Officer of HCC, said, “My fellow Directors and I are honored that such a consummate professional as Walter Duer has agreed to join our Board and management and shareholders alike will be the beneficiary of his knowledge and experience.”

HCC is an international insurance holding company and a leading specialty insurance group since 1974, based in Houston, Texas with offices across the USA and in Bermuda, England and Spain. HCC has assets of more than $5 billion, shareholders’ equity of over $1 billion and is rated AA (Very Strong) by Standard & Poor’s and A+ (Superior) by A.M. Best Company.

For more information, visit our website at www.hcch.com.

Contact: L. Byron Way, Vice President
HCC Insurance Holdings, Inc.
Telephone: (713) 690-7300

Forward-looking statements contained in this press release are made under “safe harbor” provisions of the Private Securities Litigation Reform Act of 1995 and involve a number of risks and uncertainties. The types of risks and uncertainties which may affect the Company are set forth in its periodic reports filed with the Securities and Exchange Commission.

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