
<PAGE>   1
                                                                      Exhibit 24



                    APPLIED INDUSTRIAL TECHNOLOGIES, INC.

                 Power of Attorney of Officers and Directors
                            in Connection with the
        Registration on Form S-4 of up to 2,300 Shares of Common Stock
        --------------------------------------------------------------


        The undersigned, an officer or director of APPLIED INDUSTRIAL
TECHNOLOGIES, INC., an Ohio corporation (the "Company"), which anticipates
filing with the Securities and Exchange Commission (the "Commission") under the
provisions of the Securities Act of 1993, as amended, a Registration Statement
on Form S-4 (together with any and all amendments, including post-effective
amendments, the "Registration Statement") for the purpose of registering up to
2,300,000 shares of common stock, without par value, of the Company in
connection with the merger of INVETECH Company with and into a wholly owned
subsidiary of the Company, does hereby constitute and appoint Robert C. Stinson
and Fred D. Bauer, and each of them, with full power of substitution and
resubstitution, as his or her true and lawful attorney-in-fact, to execute and
file on behalf of the undersigned, in his capacity as an officer or director of
the Company, the Registration Statement and any and all amendments, exhibits
or other documents to be filed with the Commission pertaining to the
Registration Statement or the registration contemplated thereby, with full
power and authority to do and perform any and all acts and things whatsoever
necessary or advisable to be done in connection with the foregoing, as fully
as to all intents and purposes as he could do in person, hereby ratifying and
approving the acts of said attorneys-in-fact and any of them and any such
substitution.


        Executed at ________________________, ________, this ___ day of May,
1997.

         NAME                           TITLE                        DATE
         ----                           -----                        ----

                                Chairman, Chief Executive         May ___, 1997
------------------------------  Officer and President
      John C. Dannemiller

                                Vice Chairman                     May ___, 1997
------------------------------
      John C. Robinson

                                        
                                Vice President-Finance &          May ___, 1997
------------------------------  Treasurer (Principal 
      John R. Whitten           Financial Officer)



                                Controller (Principal             May ___, 1997
------------------------------  Accounting Officer)   
      Mark O. Eisele     

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/s/ William G. Bares                      Director               May 17, 1997
------------------------------                                      
      William G. Bares                                              
                                                                    
/s/ William E. Butler                     Director               May 17, 1997
------------------------------                                      
      William E. Butler                                             
                                                                    
/s/ Russel B. Every                       Director               May 16, 1997
------------------------------                                      
      Russel B. Every                                               
                                                                    
                                                                    
/s/ L. Thomas Hiltz                       Director               May 19, 1997
------------------------------                                      
      L. Thomas Hiltz                                               
                                                                    
                                                                    
/s/ Roger D. Blackwell                    Director               May 20, 1997
------------------------------                                      
   Dr. Roger D. Blackwell                                           
                                                                    
/s/ Russel R. Gifford                     Director               May 19, 1997
------------------------------                                      
      Russell R. Gifford                                            
                                                                    
/s/ John J. Kahl                          Director               May 17, 1997
------------------------------                                      
      John J. Kahl                                                  
                                                                    
/s/   Jerry Sue Thornton                  Director               May  20, 1997
------------------------------                         
   Dr. Jerry Sue Thornton














