Abstract: A communication system connects a number of asyncrhronous remote data processing terminals, operating at different speeds, to a high speed switching and communication network. One or two telephone pairs are used as a TDM link between the terminals. The number of terminals that may be connected can be greater than the number of terminals that could be connected if all terminals were active simultaneously. A signallng function or flag is used in the system to monitor the state of each terminal. This function, which distinguishes the resting or activity of the terminals, is based on a low speed search for the idle terminals, on a detection of their change of state, and on the time sharing allocation of the system's transmission resource between the active terminals. The time sharing of the transmission resource is adaptive.