Abstract: In a communication between transmitter-side and receiver-side communication control devices, when a data communication is desired after a facsimile communication without opening a telephone line, the transmitter-side communication control device transmits a data communication shift request signal to the receiver-side communication control device based on a previous command inputted to the transmitter-side communication control device. In response to this request signal, the receiver-side communication control device switches a communication mode from a facsimile communication mode to a data communication mode, and then sends back a data communication shift acknowledge signal to the transmitter-side communication control device. In response to this acknowledge signal, the transmitter-side communication control device switches a communication mode from a facsimile communication mode to a data communication mode.