A wiping device for wiping cover plates of the headlights of motor vehicles includes a wiping arm carrying a wiper blade and swingable over the cover plate being wiped, and a drive shaft which is releasably connected to the wiping arm by means of an adapter. The wiping arm is comprised of two halves hinged to each other by a hinge the axis of which extends in a plane parallel to the cover plate being wiped. A spring is arranged between two hingeable halves of the wiping arm. The wiping device can be completely moved out from the path of light beams emitted by the headlight.