A radio base station 1 is connected together with a multi-media server 3 and a multi-media terminal unit 4 to a LAN or WAN line 100 for radio communication with radio mobile terminals 2-1 to 2-N. The radio mobile terminals 2-1 to 2-N can be switched between a power-saving mode of their part-time duty service and a normal mode of their full-time duty service. The radio base station 1 manages the radio mobile terminals 2-1 to 2-N by executing discrimination as to whether they are in the power-saving mode of the part-time duty service operation or in the normal mode of the full-time duty service operation. and when the radio mobile terminals 2-1 to 2-N are in the power-saving mode of the part-time duty service operation, it acts as an agent to execute part of the processes to be executed in the radio mobile terminals 2-1 to 2-N.