<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, 1998 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.
---------------------------
    James M. Large, Jr.               Director                   March 26, 1999


<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,
1998 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
---------------------------     Chief Executive Officer,
     Lawrence J. Toal            President and Director          March 26, 1999


<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, 1998 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
---------------------------
     Derrick D. Cephas                Director                   March 26, 1999


<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, 1998 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
---------------------------
     Frederick C. Chen                Director                   March 26, 1999


<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, 1998 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
---------------------------
   J. Barclay Collins II              Director                   March 26, 1999


<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, 1998 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
---------------------------
    Richard W. Dalrymple               Director                  March 26, 1999


<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, 1998 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
---------------------------
      James F. Fulton                 Director                   March 26, 1999


<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, 1998 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
---------------------------
     Virginia M. Kopp                 Director                   March 26, 1999


<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, 1998 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
---------------------------
       John Morning                   Director                   March 26, 1999


<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, 1998 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
----------------------------
    Margaret Osmer-McQuade             Director                   March 26, 1999


<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, 1998 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
---------------------------
    Sally Hernandez-Pinero            Director                   March 26, 1999


<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, 1998 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
---------------------------
      Paul A. Qualben                 Director                   March 26, 1999


<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, 1998 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.
---------------------------
    Eugene G. Schulz, Jr.             Director                  March 26, 1999


<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, 1998 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
---------------------------
       Howard Smith                   Director                   March 26, 1999


<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, 1998 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
---------------------------
      Norman R. Smith                 Director                   March 26, 1999


<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, 1998 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
---------------------------
       Ira T. Wender                  Director                   March 26, 1999


<PAGE>   17

                                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, 1998 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/    Fred B. Koons
---------------------------
       Fred B. Koons                  Director                   March 26, 1999