Drive system for escalators and moving walkways, comprising a set of wheels (3) carrying free-rotating rollers (4), with parallel axes to that of the wheels, and one or more shafts (5) perpendicular to the movement direction of the belt of steps or pallets (1), in which said roller wheels are mounted. The shafts (5) and wheels (3) are arranged between the moving forward way and the return way of the belt of steps or pallets (1). The wheels (3) engage through the rollers (4) with the steps or pallets (1) through engaging formations (7) of said belt of steps or pallets (1). The shafts (5) connect to a driving assembly through a transmission mechanism.