EXHIBIT 32.1

              SECTION 1350 CERTIFICATION OF CHIEF EXECUTIVE OFFICER

I, Frank C. Lin, Chief Executive Officer of Trident Microsystems, Inc. (the
"Registrant"), do hereby certify in accordance with 18 U.S.C. 1350, as adopted
pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that, based on my
knowledge:

      (1) the Annual Report on Form 10-K of the Registrant, to which this
      certification is attached as an exhibit (the "Report"), fully complies
      with the requirements of section 13(a) of the Securities Exchange Act of
      1934 (15 U.S.C. 78m); and

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

Dated: September 13, 2004                          /s/  FRANK C. LIN
                                                   -----------------------------
                                                   Frank C. Lin
                                                   Chief Executive Officer