a control circuit for an air - bag mounted in a motor vehicle comprises an acceleration sensor for producing an acceleration signal indicative of acceleration of the vehicle , an ignition timing circuit for processing the acceleration signal to predict the time when a passenger &# 39 ; s head will reach a front surface of the air - bag in fully deployed condition and producing a first air - bag deploying signal in accordance with the predicted time , and a damage discrimination circuit for processing the acceleration signal and judging the need of activation of the air - bag when the cumulative effect of the acceleration exceeds a predetermined limit . the damage discrimination circuit produces a second air - bag deploying signal when judging the need of activation of the air - bag . a so - called and circuit is further employed which actually activates the air - bag when receiving the first and second air - bag deploying signals concurrently .