A collision prevention method for motor vehicles is provided, in which method obstacles in front of the vehicle are detected by an on-board positioning system, a collision probability is calculated from the position data, and one or more responses to prevent a collision are triggered as a function of the collision probability. At least one of the responses is a preparatory measure accelerating the implementation of a command, which may be output later, to decelerate the vehicle, without the preparatory measure itself having any significant decelerating effect on the vehicle.