The system has mobile radio terminals (18). Each is associated with a main connection (11) of a transmission network. The subscriber identification of the mobile radio terminal tallies with that of the associated connection. At the beginning of each call, it transmits the subscriber identification signalising its access authorisation to the mobile system.Stationary base stations (17) receive the calls from the mobile terminals and feed them to the transmission network. A call from the mobile terminal via the base station is first fed to the network exchange to which the local exchange (DIVO) of the main connection associated with the terminal belongs. Then the call is fed to the called subscriber from this exchange.