The wireless sensor adds identification information peculiar to respective sensor modules to detection data of vibration, temperature, and soon, detected by the sensor modules respectively. The wireless sensor transmits the detection data with the identification information as a signal through a communication unit by radio waves. On the other hand, the management apparatus receiving the signal classifies and files the detection data on the basis of the identification information included in the signal. Then, the monitoring system is designed to make the management apparatus manage a plurality of wireless sensors attached to movable shafts of processing machines or the like.