Stable facsimile communications and reduced deterioration in image quality are achieved, when standard facsimile apparatuses communicate using a communication network composed a subnetwork with relatively good transmission quality such as a wire system and a subnetwork with relatively bad transmission quality such a mobile system subnetwork, both subnetworks being interspersed between the facsimile apparatuses, by inserting a pair of FAX signal converting apparatuses into the communication channel between the facsimile apparatuses for error control responsive to the quality of the channel in use.