
<PAGE>   1
                                                                      EXHIBIT 24
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                                                                      EXHIBIT 24


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<S>                                                                     <C>
GENERAL DYNAMICS CORPORATION                                            POWER OF ATTORNEY
COMMISSION FILE NUMBER 1-3671                                           REPORTS ON FORM
                       ------
IRS NO. 13-1673581                                                      10-K AND 10-Q
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                               POWER OF ATTORNEY

                     KNOW ALL MEN BY THESE PRESENTS, that each of the
undersigned Directors and/or officers of GENERAL DYNAMICS CORPORATION, a
Delaware corporation, hereby constitutes and appoints each of NICHOLAS D.
CHABRAJA, MICHAEL J. MANCUSO, PAUL A.  HESSE, as his true and lawful attorney
and agent, in the name and on behalf of the undersigned, to do any and all acts
and things and execute any and all instruments which the attorney and agent may
deem necessary or advisable to enable General Dynamics Corporation to comply
with the Securities Act of 1933, and the Exchange Act of 1934, as amended, and
any rules and regulations and requirements of the Securities and Exchange
Commission (The Commission) in respect thereof, in connection with annual
reports to the commission on form 10-K, quarterly reports on form 10-Q, and
other reports as required by General Dynamics Corporation, including
specifically, but without limiting the generality of the foregoing, the power
and authority to sign the names of the undersigned in his capacity as Director
and/or Officer of General Dynamics Corporation to reports filed with the
Securities and Exchange Commission with respect thereto, to any and all
amendments, including hereby ratifying and confirming all that the attorneys
and agents, or any of them, has done, shall do or shall cause to be done by
virtue hereof.

                     IN WITNESS WHEREOF, the undersigned have hereunto set
their hands this 5th day of February, 1997.



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   <S>                                                    <C>
   /s/    FRANK C. CARLUCCI                                  /s/    CHARLES H. GOODMAN
----------------------------------------                  ---------------------------------------
          Frank C. Carlucci                                         Charles H. Goodman


   /s/    NICHOLAS D. CHABRAJA                               /s/    JAMES R. MELLOR
-------------------------------------                     --------------------------------------------
          Nicholas D. Chabraja                                      James R. Mellor


   /s/    JAMES S. CROWN                                     /s/    GORDON R. SULLIVAN
------------------------------------------                -----------------------------------------
          James S. Crown                                            Gordon R. Sullivan


   /s/    LESTER CROWN                                       /s/    CARLISLE A. H. TROST
-------------------------------------------               ------------------------------------------
          Lester Crown                                              Carlisle A. H. Trost
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