RURAL METRO CORP /DE/
424B3, 1998-04-29
LOCAL & SUBURBAN TRANSIT & INTERURBAN HWY PASSENGER TRANS
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<PAGE>   1
                                                Filed pursuant to Rule 424(b)(3)
                                                Reg. No. 333-37393
 

                     SUPPLEMENT NO. 4 DATED APRIL 29, 1998
                      TO PROSPECTUS DATED OCTOBER 24, 1997
 
                            RURAL/METRO CORPORATION
 
                              SELLING STOCKHOLDERS
 
     The following table sets forth (i) the name of the Selling Stockholders,
who received the shares of Common Stock in connection with acquisitions by the
Company, (ii) the number of shares of Common Stock of the Company beneficially
owned by the Selling Stockholders as of April 22, 1998, and (iii) the number of
shares of Common Stock which the Selling Stockholders may offer and sell
pursuant to this Prospectus.
 
<TABLE>
<CAPTION>
                                                                                    NUMBER OF SHARES
                                                   NUMBER OF SHARES                 OF COMMON STOCK
                                                   OF COMMON STOCK                WHICH MAY BE OFFERED
NAME                                                  OWNED(1)         PERCENT      PURSUANT HERETO
- ----                                               ----------------    -------    --------------------
<S>                                                <C>                 <C>        <C>
Robert E. Ramsey, Jr. ...........................      202,276          1.43%           172,276
Horacio Artagaveytia and Jose Mateo Campomar(2)..      293,148           2.1%           146,574
</TABLE>
 
- --------------- 
(1) Except as indicated, and subject to community property laws when applicable,
    the persons named in the table above have sole voting and investment power
    with respect to all shares of Common Stock shown as beneficially owned by
    them. 
(2) Includes shares held for the benefit of Alberto Fluerquin, Carlos Mezzera,
    Renato Ribeiro, Gervasio Reyes, and Carlos Arturo Delmiro Marfetan.


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