A radar system for motor vehicles, having a radar sensor and an evaluation device for measuring distances and relative velocities of objects in the surrounding field of the vehicle, and a collision detection device, which, on the basis of the measured distances and relative velocities, recognizes an imminent collision and delivers data on the expected time of collision and the impact velocity to a precrash system. The radar sensor is switchable by the collision detection device to a velocity measurement mode in which a more precise measurement of the relative velocity is made.