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  CERTIFICATION PURSUANT TO CHAPTER 63, TITLE 18 UNITED STATES CODE SS.1350 AS
            ADOPTED BY SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002
                  ACCOMPANYING QUARTERLY REPORT ON FORM 10-Q OF
       ARCH CAPITAL GROUP LTD. FOR THE FISCAL QUARTER ENDED JUNE 30, 2002


      I, Peter A. Appel, President and Chief Executive Officer of Arch Capital
Group Ltd. (the "Company"), certify that the accompanying Quarterly Report on
Form 10-Q of the Company for the fiscal quarter ended June 30, 2002 fully
complies with the requirements of section 13(a) of the Securities Exchange Act
of 1934 and the information contained in such report fairly presents, in all
material respects, the financial condition and results of operations of the
Company.


                                    Date: August 14, 2002


                                    /s/ PETER A. APPEL
                                    --------------------------------------------
                                    Peter A. Appel
                                    President and Chief Executive Officer