EXHIBIT 99.1


              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 SEPTEMBER 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 September 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: November 14, 2002


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