A facsimile system with the body thereof usable as a subunit of a cordless telephone is disclosed. A parent unit is connected to the telephone line. A facsimile subunit is connected by radio to the parent unit. A telephone subunit is also connected by radio to the parent unit. A circuit included in the parent unit detects a signal indicating that the other party is in facsimile transmission mode. When a call signal is detected from the telephone line, the parent unit connects the line. When a CNG signal is detected, on the other hand, the parent unit connects the facsimile subunit by radio. In the case where a CNG signal is not detected, the parent unit starts the ring-up tone on the telephone subunit. An AGC circuit and a voice mute circuit are included in the parent unit.