<PAGE>
 
Exhibit 24.  Power of Attorney.

The Power of Attorney, dated February 25, 1999, is attached.
<PAGE>
 
                               THE ROUSE COMPANY
                               POWER OF ATTORNEY
                               -----------------


          KNOW ALL PERSONS BY THESE PRESENTS, that the under- signed directors
of THE ROUSE COMPANY, a Maryland corporation, constitute and appoint ANTHONY W.
DEERING, JEFFREY H. DONAHUE and BRUCE I. ROTHSCHILD, or any one of them, the
true and lawful agents and attorneys-in-fact of the undersigned, with full power
of substitution and resubstitution, and with full power and authority (i) to
sign for the undersigned, and in their respective names as directors of the
Company, the Company's Annual Report on Form 10-K for the Fiscal Year Ended
December 31, 1998 that is to be filed with the Securities and Exchange
Commission, Washington, D.C., under the Securities Exchange Act of 1934, as
amended, and the regulations promulgated thereunder, and any amendment or
amendments to such Annual Report on Form 10-K, and (ii) to file the same, with
all exhibits thereto, and all documents in connection therewith, with the
Securities and Exchange Commission, hereby ratifying and confirming all acts
taken by such agents and attorneys-in-fact, as herein authorized.

Dated:  February 25, 1999


                              /s/ David H. Benson        (SEAL)
                              --------------------------       
                              David H. Benson
<PAGE>
 
                              /s/ Jeremiah E. Casey      (SEAL)
                              --------------------------       
                              Jeremiah E. Casey


                              /s/ Mathias J. DeVito      (SEAL)
                              --------------------------       
                              Mathias J. DeVito



                              /s/ Anthony W. Deering     (SEAL)
                              --------------------------       
                              Anthony W. Deering



                              /s/ Rohit M. Desai         (SEAL)
                              --------------------------       
                              Rohit M. Desai



                              /s/ Juanita T. James       (SEAL)
                              --------------------------       
                              Juanita T. James



                              /s/ William R. Lummis      (SEAL)
                              --------------------------       
                              William R. Lummis



                              /s/ Thomas J. McHugh       (SEAL)
                              --------------------------       
                              Thomas J. McHugh



                              /s/ Hanne M. Merriman      (SEAL)
                              --------------------------       
                              Hanne M. Merriman



                              /s/ Roger W. Schipke       (SEAL)
                              --------------------------       
                              Roger W. Schipke
<PAGE>
 
                              /s/ Alexander B. Trowbridge(SEAL)
                              --------------------------       
                              Alexander B. Trowbridge



                              /s/ Gerard J. M. Vlak      (SEAL)
                              --------------------------       
                              Gerard J. M. Vlak

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