Abstract: A switching system for a network having terminal control equipment units connected to a network termination unit, in which terminal control equipment units of the same kind are connected with an exchange through a subscriber's line which has assigned to it a single subscriber number and which has a plurality of communication channels. The system including storage units for each terminal control equipment unit of the subscriber's line for storing call status of incoming calls. When a first incoming call is received, the storage units of the terminal control equipment units set respective call status for the first incoming call to a ringing state. When a second incoming call is received before a response to the first incoming call is transmitted, the storage units also set the call status for the second incoming call to a ringing state.