The cleaning device has a carrier arm (13) in a casing (12) capable of controlled movement and adjustable in height. The carrier arm carries a driven pushrod (14) with cleaning members (15) on its free end to act on the step surfaces (3) and endfaces (4) of the individual steps (2). The carrier arm can be adjusted horizontally and vertically parallel to the step and endface surfaces. The pushrod can be made to oscillate when the carrier arm moves horizontally.
