<PAGE>   1
                                                                      Exhibit 24

                                POWER OF ATTORNEY


      The undersigned hereby appoints Lawrence J. Toal and James E. Kelly or
either of the foregoing persons acting alone, each with the full power of
substitution, as his true and lawful attorney-in-fact and agent, for him and in
his name and place, to sign the name of the undersigned in the capacity or
capacities indicated below to the Annual Report of Dime Bancorp, Inc. on Form
10-K for the year ended December 31, 1997 and any and all amendments to such
Form 10-K and to file the same, with all exhibits thereto and other documents in
connection therewith, with all necessary or appropriate governmental or other
entities, including, but not limited to, the Securities and Exchange Commission
and the New York Stock Exchange, granting to such attorney-in-fact and agent
full power and authority to perform each act necessary to be done as fully to
all intents and purposes as he might do in person, hereby ratifying and
confirming all that such attorney-in-fact and agent may lawfully do or cause to
be done by virtue hereof.




      SIGNATURE                     Title                           Date


/s/ James M. Large, Jr.                              March 21, 1998
----------------------------       Director         ----------------------------
   James M. Large, Jr.
<PAGE>   2
                                POWER OF ATTORNEY


      The undersigned hereby appoints James E. Kelly as his true and lawful
attorney-in-fact and agent, for him and in his name and place, to sign the name
of the undersigned in the capacity or capacities indicated below to the Annual
Report of Dime Bancorp, Inc. on Form 10-K for the year ended December 31, 1997
and any and all amendments to such Form 10-K and to file the same, with all
exhibits thereto and other documents in connection therewith, with all necessary
or appropriate governmental or other entities, including, but not limited to,
the Securities and Exchange Commission and the New York Stock Exchange, granting
to such attorney-in-fact and agent full power and authority to perform each act
necessary to be done as fully to all intents and purposes as he might do in
person, hereby ratifying and confirming all that such attorney-in-fact and agent
may lawfully do or cause to be done by virtue hereof.




        SIGNATURE                         Title                     Date


/s/  Lawrence J. Toal                                          March 27, 1998
----------------------------       Chief Executive Officer,  -------------------
     Lawrence J. Toal              President and Director
<PAGE>   3
                                POWER OF ATTORNEY


      The undersigned hereby appoints Lawrence J. Toal and James E. Kelly or
either of the foregoing persons acting alone, each with the full power of
substitution, as his true and lawful attorney-in-fact and agent, for him and in
his name and place, to sign the name of the undersigned in the capacity or
capacities indicated below to the Annual Report of Dime Bancorp, Inc. on Form
10-K for the year ended December 31, 1997 and any and all amendments to such
Form 10-K and to file the same, with all exhibits thereto and other documents in
connection therewith, with all necessary or appropriate governmental or other
entities, including, but not limited to, the Securities and Exchange Commission
and the New York Stock Exchange, granting to such attorney-in-fact and agent
full power and authority to perform each act necessary to be done as fully to
all intents and purposes as he might do in person, hereby ratifying and
confirming all that such attorney-in-fact and agent may lawfully do or cause to
be done by virtue hereof.




         SIGNATURE                   Title                       Date


/s/  Derrick D. Cephas                                      March 27, 1998
---------------------------         Director        ----------------------------
     Derrick D. Cephas
<PAGE>   4
                                POWER OF ATTORNEY


      The undersigned hereby appoints Lawrence J. Toal and James E. Kelly or
either of the foregoing persons acting alone, each with the full power of
substitution, as his true and lawful attorney-in-fact and agent, for him and in
his name and place, to sign the name of the undersigned in the capacity or
capacities indicated below to the Annual Report of Dime Bancorp, Inc. on Form
10-K for the year ended December 31, 1997 and any and all amendments to such
Form 10-K and to file the same, with all exhibits thereto and other documents in
connection therewith, with all necessary or appropriate governmental or other
entities, including, but not limited to, the Securities and Exchange Commission
and the New York Stock Exchange, granting to such attorney-in-fact and agent
full power and authority to perform each act necessary to be done as fully to
all intents and purposes as he might do in person, hereby ratifying and
confirming all that such attorney-in-fact and agent may lawfully do or cause to
be done by virtue hereof.




        SIGNATURE                   Title                           Date


 /s/ Frederick C. Chen                                     March 26, 1998
---------------------------        Director          ---------------------------
     Frederick C. Chen
<PAGE>   5
                                POWER OF ATTORNEY


      The undersigned hereby appoints Lawrence J. Toal and James E. Kelly or
either of the foregoing persons acting alone, each with the full power of
substitution, as his true and lawful attorney-in-fact and agent, for him and in
his name and place, to sign the name of the undersigned in the capacity or
capacities indicated below to the Annual Report of Dime Bancorp, Inc. on Form
10-K for the year ended December 31, 1997 and any and all amendments to such
Form 10-K and to file the same, with all exhibits thereto and other documents in
connection therewith, with all necessary or appropriate governmental or other
entities, including, but not limited to, the Securities and Exchange Commission
and the New York Stock Exchange, granting to such attorney-in-fact and agent
full power and authority to perform each act necessary to be done as fully to
all intents and purposes as he might do in person, hereby ratifying and
confirming all that such attorney-in-fact and agent may lawfully do or cause to
be done by virtue hereof.




       SIGNATURE                     Title                          Date


/s/ J. Barclay Collins II                                   March 24, 1998
---------------------------         Director         ---------------------------
  J. Barclay Collins II
<PAGE>   6
                                POWER OF ATTORNEY


      The undersigned hereby appoints Lawrence J. Toal and James E. Kelly or
either of the foregoing persons acting alone, each with the full power of
substitution, as his true and lawful attorney-in-fact and agent, for him and in
his name and place, to sign the name of the undersigned in the capacity or
capacities indicated below to the Annual Report of Dime Bancorp, Inc. on Form
10-K for the year ended December 31, 1997 and any and all amendments to such
Form 10-K and to file the same, with all exhibits thereto and other documents in
connection therewith, with all necessary or appropriate governmental or other
entities, including, but not limited to, the Securities and Exchange Commission
and the New York Stock Exchange, granting to such attorney-in-fact and agent
full power and authority to perform each act necessary to be done as fully to
all intents and purposes as he might do in person, hereby ratifying and
confirming all that such attorney-in-fact and agent may lawfully do or cause to
be done by virtue hereof.




       SIGNATURE                    Title                        Date


/s/ Richard W. Dalrymple                                   March 23, 1998
---------------------------        Director          ---------------------------
    Richard W. Dalrymple
<PAGE>   7
                                POWER OF ATTORNEY


      The undersigned hereby appoints Lawrence J. Toal and James E. Kelly or
either of the foregoing persons acting alone, each with the full power of
substitution, as his true and lawful attorney-in-fact and agent, for him and in
his name and place, to sign the name of the undersigned in the capacity or
capacities indicated below to the Annual Report of Dime Bancorp, Inc. on Form
10-K for the year ended December 31, 1997 and any and all amendments to such
Form 10-K and to file the same, with all exhibits thereto and other documents in
connection therewith, with all necessary or appropriate governmental or other
entities, including, but not limited to, the Securities and Exchange Commission
and the New York Stock Exchange, granting to such attorney-in-fact and agent
full power and authority to perform each act necessary to be done as fully to
all intents and purposes as he might do in person, hereby ratifying and
confirming all that such attorney-in-fact and agent may lawfully do or cause to
be done by virtue hereof.




        SIGNATURE                    Title                       Date


/s/ James F. Fulton                                         March 26, 1998
---------------------------         Director         ---------------------------
    James F. Fulton
<PAGE>   8
                                POWER OF ATTORNEY


      The undersigned hereby appoints Lawrence J. Toal and James E. Kelly or
either of the foregoing persons acting alone, each with the full power of
substitution, as his true and lawful attorney-in-fact and agent, for him and in
his name and place, to sign the name of the undersigned in the capacity or
capacities indicated below to the Annual Report of Dime Bancorp, Inc. on Form
10-K for the year ended December 31, 1997 and any and all amendments to such
Form 10-K and to file the same, with all exhibits thereto and other documents in
connection therewith, with all necessary or appropriate governmental or other
entities, including, but not limited to, the Securities and Exchange Commission
and the New York Stock Exchange, granting to such attorney-in-fact and agent
full power and authority to perform each act necessary to be done as fully to
all intents and purposes as he might do in person, hereby ratifying and
confirming all that such attorney-in-fact and agent may lawfully do or cause to
be done by virtue hereof.




       SIGNATURE                     Title                          Date


/s/ Virginia M. Kopp                                   March 24, 1998
---------------------------         Director         ---------------------------
    Virginia M. Kopp
<PAGE>   9
                                POWER OF ATTORNEY


      The undersigned hereby appoints Lawrence J. Toal and James E. Kelly or
either of the foregoing persons acting alone, each with the full power of
substitution, as his true and lawful attorney-in-fact and agent, for him and in
his name and place, to sign the name of the undersigned in the capacity or
capacities indicated below to the Annual Report of Dime Bancorp, Inc. on Form
10-K for the year ended December 31, 1997 and any and all amendments to such
Form 10-K and to file the same, with all exhibits thereto and other documents in
connection therewith, with all necessary or appropriate governmental or other
entities, including, but not limited to, the Securities and Exchange Commission
and the New York Stock Exchange, granting to such attorney-in-fact and agent
full power and authority to perform each act necessary to be done as fully to
all intents and purposes as he might do in person, hereby ratifying and
confirming all that such attorney-in-fact and agent may lawfully do or cause to
be done by virtue hereof.




       SIGNATURE                     Title                          Date


/s/ John Morning                                       March 21, 1998
---------------------------         Director         ---------------------------
     John Morning
<PAGE>   10
                                POWER OF ATTORNEY


      The undersigned hereby appoints Lawrence J. Toal and James E. Kelly or
either of the foregoing persons acting alone, each with the full power of
substitution, as his true and lawful attorney-in-fact and agent, for him and in
his name and place, to sign the name of the undersigned in the capacity or
capacities indicated below to the Annual Report of Dime Bancorp, Inc. on Form
10-K for the year ended December 31, 1997 and any and all amendments to such
Form 10-K and to file the same, with all exhibits thereto and other documents in
connection therewith, with all necessary or appropriate governmental or other
entities, including, but not limited to, the Securities and Exchange Commission
and the New York Stock Exchange, granting to such attorney-in-fact and agent
full power and authority to perform each act necessary to be done as fully to
all intents and purposes as he might do in person, hereby ratifying and
confirming all that such attorney-in-fact and agent may lawfully do or cause to
be done by virtue hereof.




        SIGNATURE                     Title                         Date


/s/ Margaret Osmer-McQuade                             March 23, 1998
---------------------------          Director        ---------------------------
   Margaret Osmer-McQuade
<PAGE>   11
                                POWER OF ATTORNEY


      The undersigned hereby appoints Lawrence J. Toal and James E. Kelly or
either of the foregoing persons acting alone, each with the full power of
substitution, as his true and lawful attorney-in-fact and agent, for him and in
his name and place, to sign the name of the undersigned in the capacity or
capacities indicated below to the Annual Report of Dime Bancorp, Inc. on Form
10-K for the year ended December 31, 1997 and any and all amendments to such
Form 10-K and to file the same, with all exhibits thereto and other documents in
connection therewith, with all necessary or appropriate governmental or other
entities, including, but not limited to, the Securities and Exchange Commission
and the New York Stock Exchange, granting to such attorney-in-fact and agent
full power and authority to perform each act necessary to be done as fully to
all intents and purposes as he might do in person, hereby ratifying and
confirming all that such attorney-in-fact and agent may lawfully do or cause to
be done by virtue hereof.




        SIGNATURE                    Title                          Date


/s/ Sally Hernandez-Pinero                                 March 25, 1998
---------------------------         Director         ---------------------------
  Sally Hernandez-Pinero
<PAGE>   12
                                POWER OF ATTORNEY


      The undersigned hereby appoints Lawrence J. Toal and James E. Kelly or
either of the foregoing persons acting alone, each with the full power of
substitution, as his true and lawful attorney-in-fact and agent, for him and in
his name and place, to sign the name of the undersigned in the capacity or
capacities indicated below to the Annual Report of Dime Bancorp, Inc. on Form
10-K for the year ended December 31, 1997 and any and all amendments to such
Form 10-K and to file the same, with all exhibits thereto and other documents in
connection therewith, with all necessary or appropriate governmental or other
entities, including, but not limited to, the Securities and Exchange Commission
and the New York Stock Exchange, granting to such attorney-in-fact and agent
full power and authority to perform each act necessary to be done as fully to
all intents and purposes as he might do in person, hereby ratifying and
confirming all that such attorney-in-fact and agent may lawfully do or cause to
be done by virtue hereof.




       SIGNATURE                     Title                          Date


/s/ Paul A. Qualben                                        March 26, 1998
---------------------------         Director         ---------------------------
    Paul A. Qualben
<PAGE>   13
                                POWER OF ATTORNEY


      The undersigned hereby appoints Lawrence J. Toal and James E. Kelly or
either of the foregoing persons acting alone, each with the full power of
substitution, as his true and lawful attorney-in-fact and agent, for him and in
his name and place, to sign the name of the undersigned in the capacity or
capacities indicated below to the Annual Report of Dime Bancorp, Inc. on Form
10-K for the year ended December 31, 1997 and any and all amendments to such
Form 10-K and to file the same, with all exhibits thereto and other documents in
connection therewith, with all necessary or appropriate governmental or other
entities, including, but not limited to, the Securities and Exchange Commission
and the New York Stock Exchange, granting to such attorney-in-fact and agent
full power and authority to perform each act necessary to be done as fully to
all intents and purposes as he might do in person, hereby ratifying and
confirming all that such attorney-in-fact and agent may lawfully do or cause to
be done by virtue hereof.




        SIGNATURE                    Title                          Date


/s/ Eugene G. Schulz, Jr.                                   March 21, 1998
---------------------------         Director         ---------------------------
  Eugene G. Schulz, Jr.
<PAGE>   14
                                POWER OF ATTORNEY


      The undersigned hereby appoints Lawrence J. Toal and James E. Kelly or
either of the foregoing persons acting alone, each with the full power of
substitution, as his true and lawful attorney-in-fact and agent, for him and in
his name and place, to sign the name of the undersigned in the capacity or
capacities indicated below to the Annual Report of Dime Bancorp, Inc. on Form
10-K for the year ended December 31, 1997 and any and all amendments to such
Form 10-K and to file the same, with all exhibits thereto and other documents in
connection therewith, with all necessary or appropriate governmental or other
entities, including, but not limited to, the Securities and Exchange Commission
and the New York Stock Exchange, granting to such attorney-in-fact and agent
full power and authority to perform each act necessary to be done as fully to
all intents and purposes as he might do in person, hereby ratifying and
confirming all that such attorney-in-fact and agent may lawfully do or cause to
be done by virtue hereof.




        SIGNATURE                    Title                          Date


/s/ Howard Smith                                     March 23, 1998
---------------------------         Director         ---------------------------
      Howard Smith
<PAGE>   15
                                POWER OF ATTORNEY


      The undersigned hereby appoints Lawrence J. Toal and James E. Kelly or
either of the foregoing persons acting alone, each with the full power of
substitution, as his true and lawful attorney-in-fact and agent, for him and in
his name and place, to sign the name of the undersigned in the capacity or
capacities indicated below to the Annual Report of Dime Bancorp, Inc. on Form
10-K for the year ended December 31, 1997 and any and all amendments to such
Form 10-K and to file the same, with all exhibits thereto and other documents in
connection therewith, with all necessary or appropriate governmental or other
entities, including, but not limited to, the Securities and Exchange Commission
and the New York Stock Exchange, granting to such attorney-in-fact and agent
full power and authority to perform each act necessary to be done as fully to
all intents and purposes as he might do in person, hereby ratifying and
confirming all that such attorney-in-fact and agent may lawfully do or cause to
be done by virtue hereof.




         SIGNATURE                   Title                          Date


/s/   Norman R. Smith                                 March 25, 1998
---------------------------         Director         ---------------------------
      Norman R. Smith
<PAGE>   16
                                POWER OF ATTORNEY


      The undersigned hereby appoints Lawrence J. Toal and James E. Kelly or
either of the foregoing persons acting alone, each with the full power of
substitution, as his true and lawful attorney-in-fact and agent, for him and in
his name and place, to sign the name of the undersigned in the capacity or
capacities indicated below to the Annual Report of Dime Bancorp, Inc. on Form
10-K for the year ended December 31, 1997 and any and all amendments to such
Form 10-K and to file the same, with all exhibits thereto and other documents in
connection therewith, with all necessary or appropriate governmental or other
entities, including, but not limited to, the Securities and Exchange Commission
and the New York Stock Exchange, granting to such attorney-in-fact and agent
full power and authority to perform each act necessary to be done as fully to
all intents and purposes as he might do in person, hereby ratifying and
confirming all that such attorney-in-fact and agent may lawfully do or cause to
be done by virtue hereof.




        SIGNATURE                    Title                          Date


/s/   Ira T. Wender                                   March 21, 1998
---------------------------         Director         ---------------------------
     Ira T. Wender