In a radio alarm signaling system with a central station (Z) and a plurality of bidirectional (BT1 to BT5) and unidirectional (UT1, UT2) subscribers, the unidirectional subscribers (UT1, UT2) attempt to send messages via one of the bidirectional subscribers (BT1 to BT5) to the central station. In this case the message sent by a unidirectional subscriber (UT2) is received by all bidirectional subscribers (BT1, BT2, BT5) in its radio coverage area. Each bidirectional subscriber that has received this message waits until a time slot individually assigned to it before forwarding the message. During the wait time each of these bidirectional subscribers (BT1, BT2, BT5) monitors the radio channel to see whether another subscriber has already forwarded the message. If this is the case it suppresses its own forwarding. This ensures that only one of the bidirectional subscribers (BT1) forwards the message so that no overloading of the radio system occurs.