An engine control unit comprising: a stationary-state idling stop controller that automatically stops an engine mounted in a vehicle during a stationary-state of the vehicle; and an input connected to a speed sensor , that detects a speed (V) of the vehicle; wherein the stationary-state idling stop controller automatically stops the engine after the engine is started and upon the establishment of a stationary-state idling stop condition corresponding to the stop of the vehicle, whereas the stationary-state idling stop controller is not permitted until the speed (V) of the vehicle exceeds a first speed (V 1 ) after the idling start; and a coasting-state idling stop controller that automatically stops the engine during a coasting state of the vehicle, wherein the coasting-state idling stop controller automatically stops the engine after the engine is started and during the coasting state of the vehicle, when the speed (V) of the vehicle is falling below a third speed (V 3 ) ; the engine control unit being characterized in that the coasting-state idling stop controller is permitted when the speed (V) of the vehicle is exceeding a second speed (V 2 ) higher than the first speed (V 2 ) and higher than the third speed (V 3 ), when the engine has been not stopped during the latest vehicle coasting or when the vehicle has been stopped since the latest vehicle coasting; in that the coasting-state idling stop controller is permitted when the speed (V) of the vehicle is exceeding fourth speed (V 4 ) higher than the second speed (V 2 ), when the engine has been stopped during the latest vehicle coasting and when the vehicle has not been stopped since the latest vehicle coasting; and in that the coasting-state idling stop controller is not permitted otherwise. a stationary-state idling stop controller that automatically stops an engine mounted in a vehicle during a stationary-state of the vehicle; and an input connected to a speed sensor , that detects a speed (V) of the vehicle; wherein the stationary-state idling stop controller automatically stops the engine after the engine is started and upon the establishment of a stationary-state idling stop condition corresponding to the stop of the vehicle, whereas the stationary-state idling stop controller is not permitted until the speed (V) of the vehicle exceeds a first speed (V 1 ) after the idling start; and a coasting-state idling stop controller that automatically stops the engine during a coasting state of the vehicle, wherein the coasting-state idling stop controller automatically stops the engine after the engine is started and during the coasting state of the vehicle, when the speed (V) of the vehicle is falling below a third speed (V 3 ) ; the engine control unit being characterized in that the coasting-state idling stop controller is permitted when the speed (V) of the vehicle is exceeding a second speed (V 2 ) higher than the first speed (V 2 ) and higher than the third speed (V 3 ), when the engine has been not stopped during the latest vehicle coasting or when the vehicle has been stopped since the latest vehicle coasting; in that the coasting-state idling stop controller is permitted when the speed (V) of the vehicle is exceeding fourth speed (V 4 ) higher than the second speed (V 2 ), when the engine has been stopped during the latest vehicle coasting and when the vehicle has not been stopped since the latest vehicle coasting; and in that the coasting-state idling stop controller is not permitted otherwise. <EOS>