A communication apparatus which prevents one host computer from occupying the apparatus and enables a user of the host computer having sent a processing request thereto to quickly know a processing result. A connection request is accepted from one of a plurality of host computers. In response to the accepted connection request, the host computer having sent the connection request is connected, and a process requested by the connected host computer is executed. Information indicative of the connected host computer is stored. Control is performed such that a reconnection request from the host computer indicated by the stored information is accepted with priority over connection requests from other host computers.