In the case of a windshield wiper system with two opposite wipers 1, 2, 4, 5 and two reversing motors 6, 7, the risk of a collision of the wipers can be diminished greatly in that a defined phase displacement is generated between the wiping movements of the two wipers, which are driven in a reversing manner, with the aid of the lever mechanism 8 associated with the reversing motors, and said phase displacement is arranged so that the one wiper is leading relative to the other wiper in the first wiping direction and lagging in the second wiping direction.