Adaptive cruise control system and method for automotive vehicle with inter-vehicle distance control function

In an adaptive cruise control method for an automotive vehicle, an inter-vehicle distance between the vehicle and a preceding vehicle which is traveling ahead of the vehicle is detected. The velocity of at least one of the vehicle and the preceding vehicle is detected. The traveling state of the vehicle is controlled on the basis of the detected inter-vehicle distance and a target inter-vehicle distance (D*). A delay (based on time constant to Fig. 15) is provided for one of the detected velocities of the vehicle and the preceding vehicle which is used to set the target inter-vehicle distance (D*) at a time of a detection of one of the velocities of the vehicle and the preceding vehicle which is used to set the target inter-vehicle distance. The target inter-vehicle distance is set on the basis of the detected velocity of one of the vehicle and the preceding vehicle for which the delay is provided.