Wireless device monitoring system

In a wireless device monitoring system including a mobile telephone (1) and an authentication apparatus (2), a controller (20) of the authentication apparatus (2) repeatedly executes a distance detection processing based on a received level of a received wireless signal and an authentication processing based on authentication data included in the received wireless signal continuously at a first communication interval (T1) and a second communication interval (T2), respectively, and outputs an alarm signal or executes a predetermined control processing when a true counterpart electronic apparatus is not present or when the true counterpart electronic apparatus is apart from the electronic apparatus by a distance longer than the predetermined threshold distance. When a first communication time (T11) for the distance detection processing is shorter than a second communication time (T12) for the authentication processing, the T1 and the T2 are set to satisfy T1