The safety of occupants in a vehicle is increased by avoiding an unnecessary deployment of a safety device, such as an air bag in the vehicle. For this purpose the trigger signal for deploying the safety device is generated either in response to a vehicle motion signal exceeding a high threshold level or in response to the vehicle motion signal exceeding a low threshold level as determined by a precrash signal (S1) followed by a crash signal (S2) preferably within a limited time duration (TMAX). For this purpose the signals (S1) and (S2) are logically linked and the resulting signal at the output of an AND-gate or at the output of a timing circuit determines whether the vehicle motion signal is compared with the high threshold level or with the low threshold level for generating the trigger or deployment signal (DS). Only when this double condition occurs, is the trigger threshold lowered for deploying the safety device. An optical sensor is preferably used as the crash signal generator.