An alternating drive for wheeled vehicles comprises two opposite pedals which can move on a circular path about a pedal shaft secured on the cycle frame. The alternating drive is characterized in that it is equipped with two cranks (26, 27; 26a, 27a; 26b, 27b) which can be moved within a predetermined oscillating angle range about an auxiliary shaft (25) secured to the frame (10). Between the cranks (26, 27; 26a, 27a; 26b; 27b) and the pedals (21) is a driver connection which transforms the circular motion into an alternating oscillating motion with phases mutually offset by a half oscillation period. Disposed on each side of the axle (50) of the driven wheel (12) is a free-wheel mechanism (56, 57). The free-wheel mechanisms (56, 57) lock in opposite directions and are connected to the individual cranks (26, 27; 26a, 27a; 26b, 27b) by mutually independent traction elements (29; 82, 83).