<PAGE>
 
                                                                      Exhibit 24



                                POWER OF ATTORNEY
                                -----------------



         I hereby appoint JAMES N. ROETHE, JEFFREY R. LAPIC, and CHERYL SOROKIN,
and each of them, my attorneys-in-fact, each with full power of substitution, to
sign for me as a Director of BankAmerica Corporation and file with the
Securities and Exchange Commission the Corporation's Form 10-K annual report for
1997, and any amendments.

Dated:  1/28, 1998



                               /s/ JOSEPH F. ALIBRANDI
                              -------------------------
                                  Joseph F. Alibrandi



[BAC-Form 10-K: Director]

<PAGE>
 
                                                                      Exhibit 24
 
                              POWER OF ATTORNEY
                              -----------------



         I hereby appoint JAMES N. ROETHE, JEFFREY R. LAPIC, and CHERYL SOROKIN,
and each of them, my attorneys-in-fact, each with full power of substitution, to
sign for me as a Director of BankAmerica Corporation and file with the
Securities and Exchange Commission the Corporation's Form 10-K annual report for
1997, and any amendments.

Dated: 2/1, 1998


                             /s/ PETER B. BEDFORD
                             --------------------
                                 Peter B. Bedford



[BAC-Form 10-K: Director]

<PAGE>
 
                                                                      Exhibit 24
 
                              POWER OF ATTORNEY
                              -----------------



         I hereby appoint JAMES N. ROETHE, JEFFREY R. LAPIC, and CHERYL SOROKIN,
and each of them, my attorneys-in-fact, each with full power of substitution, to
sign for me as a Director of BankAmerica Corporation and file with the
Securities and Exchange Commission the Corporation's Form 10-K annual report for
1997, and any amendments.

Dated: Jan 29, 1998



                             /s/ RICHARD A. CLARKE
                             ---------------------
                                 Richard A. Clarke



[BAC-Form 10-K: Director]

<PAGE>
 
                                                                      Exhibit 24
 
                              POWER OF ATTORNEY
                              -----------------



         I hereby appoint JAMES N. ROETHE, JEFFREY R. LAPIC, and CHERYL SOROKIN,
and each of them, my attorneys-in-fact, each with full power of substitution, to
sign for me as Chairman of the Board, President, and Chief Executive Officer of
BankAmerica Corporation and file with the Securities and Exchange Commission the
Corporation's Form 10-K annual report for 1997, and any amendments.

Dated: 2/2, 1998



                             /s/ DAVID A. COULTER
                             --------------------
                                 David A. Coulter



[BAC-Form 10-K: Principal Executive Officer]

<PAGE>
 
                                                                      Exhibit 24
 
                              POWER OF ATTORNEY
                              -----------------



         I hereby appoint JAMES N. ROETHE, JEFFREY R. LAPIC, and CHERYL SOROKIN,
and each of them, my attorneys-in-fact, each with full power of substitution, to
sign for me as a Director of BankAmerica Corporation and file with the
Securities and Exchange Commission the Corporation's Form 10-K annual report for
1997, and any amendments.

Dated: 2/2, 1998



                             /s/ TIMM F. CRULL
                             -----------------
                                 Timm F. Crull



[BAC-Form 10-K: Director]

<PAGE>
 
                                                                      Exhibit 24
 
                              POWER OF ATTORNEY
                              -----------------



         I hereby appoint JAMES N. ROETHE, JEFFREY R. LAPIC, and CHERYL SOROKIN,
and each of them, my attorneys-in-fact, each with full power of substitution, to
sign for me as a Director of BankAmerica Corporation and file with the
Securities and Exchange Commission the Corporation's Form 10-K annual report for
1997, and any amendments.

Dated: 2/2, 1998



                             /s/ KATHLEEN FELDSTEIN
                             ----------------------
                                 Kathleen Feldstein



[BAC-Form 10-K: Director]

<PAGE>
 
                                                                      Exhibit 24
 
                              POWER OF ATTORNEY
                              -----------------



         I hereby appoint JAMES N. ROETHE, JEFFREY R. LAPIC, and CHERYL SOROKIN,
and each of them, my attorneys-in-fact, each with full power of substitution, to
sign for me as a Director of BankAmerica Corporation and file with the
Securities and Exchange Commission the Corporation's Form 10-K annual report for
1997, and any amendments.

Dated:  1/30, 1998



                             /s/ DONALD E. GUINN
                             -------------------
                                 Donald E. Guinn



[BAC-Form 10-K: Director]

<PAGE>
 
                                                                      Exhibit 24
 
                              POWER OF ATTORNEY
                              -----------------



         I hereby appoint JAMES N. ROETHE, JEFFREY R. LAPIC, and CHERYL SOROKIN,
and each of them, my attorneys-in-fact, each with full power of substitution, to
sign for me as an Executive Vice President and Chief Accounting Officer of
BankAmerica Corporation and file with the Securities and Exchange Commission the
Corporation's Form 10-K annual report for 1997, and any amendments.

Dated: February 2, 1998



                             /s/ JOHN J. HIGGINS
                             -------------------
                                 John J. Higgins



[BAC-Form 10-K: Principal Accounting Officer]

<PAGE>
 
                                                                      Exhibit 24
 
                              POWER OF ATTORNEY
                              -----------------



         I hereby appoint JAMES N. ROETHE, JEFFREY R. LAPIC, and CHERYL SOROKIN,
and each of them, my attorneys-in-fact, each with full power of substitution, to
sign for me as a Director of BankAmerica Corporation and file with the
Securities and Exchange Commission the Corporation's Form 10-K annual report for
1997, and any amendments.

Dated: 1/30, 1998



                             /s/ FRANK L. HOPE, JR.
                             ----------------------
                                 Frank L. Hope, Jr.



[BAC-Form 10-K: Director]

<PAGE>
 
                                                                      Exhibit 24
 
                              POWER OF ATTORNEY
                              -----------------



         I hereby appoint JAMES N. ROETHE, JEFFREY R. LAPIC, and CHERYL SOROKIN,
and each of them, my attorneys-in-fact, each with full power of substitution, to
sign for me as a Director of BankAmerica Corporation and file with the
Securities and Exchange Commission the Corporation's Form 10-K annual report for
1997, and any amendments.

Dated: 2/2, 1998


                             /s/ WALTER E. MASSEY
                             --------------------
                                 Walter E. Massey



[BAC-Form 10-K: Director]

<PAGE>
 
                                                                      Exhibit 24
 
                              POWER OF ATTORNEY
                              -----------------



         I hereby appoint JAMES N. ROETHE, JEFFREY R. LAPIC, and CHERYL SOROKIN,
and each of them, my attorneys-in-fact, each with full power of substitution, to
sign for me as Vice Chairman and Chief Financial Officer of BankAmerica
Corporation and file with the Securities and Exchange Commission the
Corporation's Form 10-K annual report for 1997, and any amendments.

Dated: 2/2, 1998



                             /s/ MICHAEL E. O'NEILL
                             ----------------------
                                 Michael E. O'Neill



[BAC-Form 10-K: Principal Financial Officer]

<PAGE>
 
                                                                      Exhibit 24
 
                              POWER OF ATTORNEY
                              -----------------



         I hereby appoint JAMES N. ROETHE, JEFFREY R. LAPIC, and CHERYL SOROKIN,
and each of them, my attorneys-in-fact, each with full power of substitution, to
sign for me as a Director of BankAmerica Corporation and file with the
Securities and Exchange Commission the Corporation's Form 10-K annual report for
1997, and any amendments.

Dated: Jan. 29, 1998



                             /s/ JOHN M. RICHMAN
                             -------------------
                                 John M. Richman



[BAC-Form 10-K: Director]

<PAGE>
 
                                                                      Exhibit 24
 
                              POWER OF ATTORNEY
                              -----------------



         I hereby appoint JAMES N. ROETHE, JEFFREY R. LAPIC, and CHERYL SOROKIN,
and each of them, my attorneys-in-fact, each with full power of substitution, to
sign for me as a Director of BankAmerica Corporation and file with the
Securities and Exchange Commission the Corporation's Form 10-K annual report for
1997, and any amendments.

Dated: 2/2, 1998



                             /s/ SANFORD R. ROBERTSON
                             ------------------------
                                 Sanford R. Robertson



[BAC-Form 10-K: Director]

<PAGE>
 
                                                                      Exhibit 24
 
                              POWER OF ATTORNEY
                              -----------------



         I hereby appoint JAMES N. ROETHE, JEFFREY R. LAPIC, and CHERYL SOROKIN,
and each of them, my attorneys-in-fact, each with full power of substitution, to
sign for me as a Director of BankAmerica Corporation and file with the
Securities and Exchange Commission the Corporation's Form 10-K annual report for
1997, and any amendments.

Dated: 1/30, 1998



                             /s/ RICHARD M. ROSENBERG
                             ------------------------
                                 Richard M. Rosenberg



[BAC-Form 10-K: Director]

<PAGE>
 
                                                                      Exhibit 24
 
                              POWER OF ATTORNEY
                              -----------------



         I hereby appoint JAMES N. ROETHE, JEFFREY R. LAPIC, and CHERYL SOROKIN,
and each of them, my attorneys-in-fact, each with full power of substitution, to
sign for me as a Director of BankAmerica Corporation and file with the
Securities and Exchange Commission the Corporation's Form 10-K annual report for
1997, and any amendments.

Dated: 2/2, 1998


                             /s/ A. MICHAEL SPENCE
                             ---------------------
                                 A. Michael Spence



[BAC-Form 10-K: Director]

<PAGE>
 
                                                                      Exhibit 24
 
                              POWER OF ATTORNEY
                              -----------------



         I hereby appoint JAMES N. ROETHE, JEFFREY R. LAPIC, and CHERYL SOROKIN,
and each of them, my attorneys-in-fact, each with full power of substitution, to
sign for me as a Director of BankAmerica Corporation and file with the
Securities and Exchange Commission the Corporation's Form 10-K annual report for
1997, and any amendments.

Dated: 2/2, 1998



                             /s/ SOLOMON D. TRUJILLO
                             -----------------------
                                 Solomon D. Trujillo



[BAC-Form 10-K: Director]