A calling side communication apparatus includes a communication function executing means 11, a non-real time call sending means 12 for sending, in accordance with user operation, a non-real time call which is a request of telephone call which continues until a user at the other side responds or until a predetermined cancellation condition is satisfied. A called side communication apparatus includes a communication function executing means 21, a non-real time call receiving means 22 for receiving the non-real time call without entailing forcible ringing, a receiving call displaying means 23 for displaying, to a user, information about the non-real time call currently in the call reception state, and a non-real time call responding means 24 for establishing a telephone call or a data communication with the communication apparatus that sent the non-real time call, in accordance with a response operation given by the user in reply to the non-real time call currently in the call reception state.