Adaptive cruise and inter-vehicle distance control system for vehicle

An adaptive cruise control (ACC) system for a host-vehicle controls one of a driving force and a brake hydraulic pressure according to a command vehicle speed calculated on the basis of an inter-vehicle distance and a host-vehicle speed. The ACC system gradually decreases a deceleration of the host-vehicle according to an approach of the host-vehicle speed toward a control-cancel vehicle speed when the host-vehicle speed becomes lower than or equal to a gradual-deceleration starting vehicle speed during a period of decreasing the host-vehicle speed toward the control-cancel vehicle speed, so that the deceleration takes a value near zero when the host-vehicle speed reaches the control-cancel vehicle speed.