EXHIBIT 32

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report of Apex Silver Mines Limited (the “Company”) on Form 10-Q for the quarter ended September 30, 2008 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), the undersigned hereby certifies, pursuant to 18 U.S.C. §1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, that:

(1) The Report fully complies with the requirements of section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(2) The information contained in the Report fairly presents, in all material respects, the financial condition and result of operations of the Company.

/s/ Jeffrey G. Clevenger

Jeffrey G. Clevenger

President and Chief Executive Officer

November 10, 2008

/s/ Gerald J. Malys

Gerald J. Malys

Senior Vice President and Chief Financial Officer

November 10, 2008