Abstract: Apparatus provides a signal to an operator of a following vehicle when it is necessary to take appropriate action to avoid coming within a predetermined distance of a lead vehicle proceeding in the same direction. From initial predicted forward velocities and distances of the lead and following vehicles, the signal apparatus (1) derives subsequent predicted velocities and positions of the lead and following vehicles and a subsequent predicted distance D(t) between the lead vehicle and the following vehicle after a projected short time interval while assuming a predetermined braking action of the following vehicle (2), derives and compares the subsequent predicted distance D(t) between the lead vehicle and the following vehicle with a least distance D.sub.LEAST, and (3) sets the least distance D.sub.LEAST equal to the subsequent predicted distance D(t) between the lead vehicle and the following vehicle if the latter is smaller.