Abstract: Plural transmitters, which transmit signals to a common receiver, transmit their signals in a fixed time-staggered pattern. As a result, the individual signals which are transmitted by the respective transmitters do not interfere with one another or influence one another. Between the fixed time-staggered signals, which are sent out, for example, as standard signals to facilitate routinelike monitoring, signals of a higher priority, for example alarm signals, can be transmitted without any time delay. This is particularly suited for use in connection with a personal security and monitoring system, in which the function monitoring of the unit and the wireless connection between several transmitters and a receiving center must constantly be monitored, and signals of a higher priority, namely alarm signals, are transmitted without delay.