To provide a multiplex communication system where nodes can reliably shift to a sleep state even though the system has a very simple structure and even if abnormal conditions occur in any node, multiple nodes communicate with each other through a communication network, and when the individual nodes are in a state of being unable to shift to a sleep state, they set a sleep disable bit in signals to be transmitted and transmit them. When they become able to shift to the sleep state, the individual nodes confirm that they have not yet received an active sleep disable bit sent from other nodes continuously over a predetermined period of time or more. Thereafter, each individual node proceeds to the sleep state. According to the system, the individual nodes can proceed to the sleep state by simply determining non-transmission of the sleep disable bit from other nodes even in the presence of nodes deactivated due to failures.