In the apparatus for signalling an alarm, for example, in a gas or fire detecting installation, a detector is reset after a first response and the time duration until the next-following detector response is determined and classified with respect to three classes of time periods. When the time duration until the further detector response is beyond a predetermined upper or outer time limit, no alarm signal is released and the apparatus returns into its original state. When the further detector response occurs between two time limits, the alarm is immediately signalled. When the further detector response occurs prior to a lower one of the two time limits, there is carried out still one further test during which the detector is once again reset. The alarm signal will only be released if an additional further detector response is still observed prior to the upper time limit. In this manner the reliability of alarm signalling can be enhanced and the frequency of the occurrence of false alarms, particularly due to the occurrence of short-time or brief spurious conditions, can be significantly reduced.