PURPOSE: To cut fuel accurately at deceleration by deactuating an idling rotation accelerator, which is incorporated with a slow-cut device at deceleration, when an cooler is in use over a set rotating speed.

CONSTITUTION: A speed switch 4, a throttle opening switch 6, a neurtal switch 8, and a clutch switch 9 are connected to a slow-cut solenoid valve 3, which shuts off fuel from a slow port, to shuts off fuel at deceleration when a gear is thrown in at a constant speed. Also, a solenoid valve 15 for idling speed acceleration is interlocked with an air conditioning switch 11 thorugh a relay 20. The relay 20 which is connected with the speed switch 4 is switched at deceleration over a constant speed to deactuate a valve 15.