An engine control apparatus and method can prevent hunting during engine deceleration in a reliable manner, thereby improving the driving sensation or comfort of the driver of a vehicle. An air/fuel mixture is supplied to engine cylinders through an intake passage with a throttle valve disposed therein, and a bypass passage with an air valve disposed therein is connected with the intake passage for bypassing the throttle valve to supply auxiliary air to the cylinders. An electronic control unit includes a deceleration determining section for determining whether the engine is decelerating and for determining whether the rotational speed of the engine is equal to or less than a predetermined reference value, a deceleration processing section for performing a deceleration processing whereby the amount of auxiliary air is swiftly increased to a maximum and then gradually decreased when the engine rotational speed becomes equal to or less than the predetermined reference value during engine deceleration, and a deceleration processing disabling section for determining whether a deceleration processing is being performed and for disabling the deceleration determining section when the deceleration processing is being performed. Thus, even if the engine rotational speed, having once fallen below the reference speed, rises above it and then falls below it during the deceleration processing, the deceleration processing disabling section disables the decelerating determining section whereby the engine rotational speed can be gradually and smoothly reduced to an idling speed without hunting.