<PAGE>   1

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

     The undersigned, each being a Director of Applied Extrusion Technologies,
Inc. ("AET"), does hereby constitute and appoint Thomas E. Williams his true and
lawful attorney and agent, with power of substitution or resubstitution, to do
any and all acts and things and to execute any and all instruments that said
attorney and agent may deem necessary or advisable or which may required to
enable AET to comply with the Securities Exchange Act of 1934, as amended (the
"Act"), and any rules, regulations or requirements of the Securities and
Exchange Commission in respect thereof, in connection with the filing of AET's
Annual Report on Form 10-K for the fiscal year ended September 30, 1996,
including specifically without limiting the generality of the foregoing, the
power and authority to sign in the name of and on behalf of the undersigned as a
Director of AET. The undersigned does hereby ratify and confirm all that said
attorney and agent shall do or cause to be done by virtue thereof.

<TABLE>
<CAPTION>
Signature                           Title                        Date
---------                           -----                        ----
<S>                                 <C>                          <C>
/s/ Amin J. Khoury                                               December 4, 1996
-------------------------           Chairman of the Board        ---------------
Amin J. Khoury                     


/s/ Paul W. Marshall                                             December 4, 1996
-------------------------           Director                     ---------------
Paul W. Marshall                                                                
                                                                                
                                                                                
/s/ Richard G. Hamermesh                                         December 4, 1996        
-------------------------           Director                     ---------------
Richard G. Hamermesh                                                            
                                                                                
                                                                                
/s/ Mark Harmeling                                               December 4, 1996   
-------------------------           Director                     ---------------
Mark Harmeling                                                                 
                                                                                
                                                                                
/s/ Nader A. Golestaneh                                          December 4, 1996        
-------------------------           Director                     ---------------
Nader A. Golestaneh                                                             
                                                                                
                                                                                
/s/ Joseph J. O'Donnell                                          December 4, 1996
-------------------------           Director                     ---------------
Joseph J. O'Donnell                                                             
                                                                                
                                                                                
/s/ Hansjorg Wyss                                                December 4, 1996        
-------------------------           Director                     ---------------
Hansjorg Wyss                                                                   
                                                                                
                                                                                
/s/ Richard H. Beeby                                             December 3, 1996        
-------------------------           Director                     ---------------
Richard H. Beeby                                                                

</TABLE>