A cleaning device for a surface of a cylinder of a printer and/or a copier includes a cylindrical cleaning element which can be rotated by at least one drive and which includes a cleaning fitting on its outer periphery, and a suction or suctioner conducting at least one suction medium with at least one suction channel aligned towards the outer periphery of the cleaning element and extending along the longitudinal alignment of the cleaning element. In order to achieve a simple technical structure and a low maintenance effort apart from a good cleaning result and reliable dirt removal, a suction slit extending longitudinally of the suction channel is aligned towards the cleaning element opens into the suction channel tangentially to the suction channel cross section.