To control a modem which superposes a digital signal on a subscriber line and its telephone set system not to close a loop of a telephone line during communication of a data terminal.

The modem which is equipped with an interface accommodating a data terminal and a subscriber line interface connected as a terminal to a telephone network and communicates with opposite-side equipment by encoding and modulating data from the data terminal into a signal of a frequency band not overlapping with a frequency band for use of telephone and superposing it on the telephone network is equipped with a subscriber line interface accommodating a telephone set and a control line interface communicating control information with the telephone set; and the control line transmits notice of the start and end of communication of the data terminal to the telephone set, which recognizes a hook operation and dial button depression by a telephone set user.