The cleaning device has an automatically driven cleaning roller with textile covering (27) and elastic jacket (28). It removes the silicone particles which arise on the printing forme cylinder or may be used for cleaning other rollers or cylinders. When removing the silicone particles the cleaning roller (26) is moved at a circumferential speed which is small compared to that of the printing forme cylinder. The printing forme cylinder and the cleaning roller can be driven oppositely or in the same direction. The cleaning roller can be supplied with cleaning fluid from a wetting device (30).