A radio communication system has a fixed radio communication unit that sends a request for authentication, and portable radio communication units. Each portable radio communication unit receives the request, transmits presence information to the portable radio communication units, and determines whether presence information from more than one portable radio communication unit was received. When it is determined that the presence information from only one portable radio communication unit was received, the portable radio communication unit transmits an answer to the fixed radio communication unit. When it is determined that presence information from more than one portable radio communication unit was received, each portable radio communication unit sets a response delay time by a specified setting method, and after a lapse of the response delay time, an answer is sent to the fixed radio communication unit. The fixed radio communication unit authenticates the portable radio communication units that sent the answer.