Drive units for movable platforms for supporting and transporting motor-vehicles for automated parking systems having one or more overlapped floors, adapted to actuate and to transport said movable platforms toward and from parking positions selected in advance. There are provided two drive units (10) identical to each other, adapted to displace the movable platforms (11), one in the longitudinal direction and the other one in the transversal direction of each parking floor, each one of which comprises a lifting and sliding unit (14) constituted by a rotating roller (19) and a bellows element (16), and an actuating unit (15) constituted by a gearmotor (36) and movement transmission members (33, 34, 35) for the lifting and sliding unit (14).