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                                                                    EXHIBIT 32.1

                    CERTIFICATION OF CHIEF EXECUTIVE OFFICER

      Pursuant to 18 U.S.C. Section 1350, as created by Section 906 of the
Sarbanes-Oxley Act of 2002, the undersigned officer of BioMed Realty Trust, Inc.
(the "Company") herebY certifies, to such officer's knowledge, that:

      (i)   the accompanying Quarterly Report on Form 10-Q of the Company for
   the quarterly period ended June 30, 2004 (the "Report") fully complies with
   the requirements of Section 13(a) or Section 15(d), as applicable, of the
   Securities Exchange Act of 1934, as amended; and

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

   Dated: September 20, 2004                    /s/ ALAN D. GOLD
                                                --------------------------------
                                                Alan D. Gold
                                                Chief Executive Officer

      The foregoing certification is being furnished solely to accompany the
Report pursuant to 18 U.S.C. Section 1350, and is not being filed for purposes
of Section 18 of the Securities Exchange Act of 1934, as amended, and is not to
be incorporated by reference into any filing of the Company, whether made before
or after the date hereof, regardless of any general incorporation language in
such filing. A signed original of this written statement required by Section 906
has been provided to the Company and will be retained by the Company and
furnished to the Securities and Exchange Commission or its staff upon request.

                    CERTIFICATION OF CHIEF FINANCIAL OFFICER

      Pursuant to 18 U.S.C. Section 1350, as created by Section 906 of the
Sarbanes-Oxley Act of 2002, the undersigned officer of BioMed Realty Trust, Inc.
(the "Company") hereby certifies, to such officer's knowledge, that:

      (i)   the accompanying Quarterly Report on Form 10-Q of the Company for
   the quarterly period ended June 30, 2004 (the "Report") fully complies with
   the requirements of Section 13(a) or Section 15(d), as applicable, of the
   Securities Exchange Act of 1934, as amended; and

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

   Dated: September 20, 2004                    /s/ JOHN F. WILSON, II
                                                --------------------------------
                                                John F. Wilson, II
                                                Chief Financial Officer

      The foregoing certification is being furnished solely to accompany the
Report pursuant to 18 U.S.C. Section 1350, and is not being filed for purposes
of Section 18 of the Securities Exchange Act of 1934, as amended, and is not to
be incorporated by reference into any filing of the Company, whether made before
or after the date hereof, regardless of any general incorporation language in
such filing. A signed original of this written statement required by Section 906
has been provided to the Company and will be retained by the Company and
furnished to the Securities and Exchange Commission or its staff upon request.