Disclosed is an apparatus having an air control valve for introducing an amount of air into the intake system of an internal combustion engine when the engine begins to decelerate, for preventing after-fire of an unburnt air-fuel mixture in the catalytic converter arranged in an exhaust pipe of the engine. The apparatus further includes a temperature detecting valve adapted for stopping the operation of the flow control valve during engine warm-up operations. Therefore, introduction of air into the intake system is stopped even if the engine begins to decelerate and, also, a proper engine warm-up operation can be carried out.