Exhibit 32.1

CERTIFICATIONS OF CHIEF EXECUTIVE OFFICER AND CHIEF FINANCIAL OFFICER
PURSUANT TO
RULE 13a-14(b)/Rule 15d-14(b) OF THE SECURITIES EXCHANGE ACT OF 1934, AS AMENDED
AND 18 U.S.C. SECTION 1350, AS ADOPTED PURSUANT TO
SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

    In connection with the Annual Report on Form 10-K of Capstone Turbine Corporation (the “Company”) for the year ended March 31, 2004, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), John Tucker, Chief Executive Officer of the Company, and Karen Clark, Chief Financial Officer of the Company, certify, pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 (Subsections (a) and (b) of Section 1350, Chapter 63 of Title 18, United States Code), that the Report complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934 and that information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.
         
     
  By:   /s/ JOHN TUCKER    
    John Tucker   
    President and Chief Executive Officer   
 
         
     
  By:   /s/ KAREN CLARK    
    Karen Clark   
    Chief Financial Officer   
 

Date: June 14, 2004

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