A complete cleaning system for printing cylinders within a rotary printing press, by which a reactive erasing of ink-bearing layers, including the removal of filling materials from a gravure printing form, and a cleaning of ink from all form and transfer cylinders are possible during the printing process or during printing pauses. At least one erasing device is provided which emits a jet of water under pressure that can be directed against the corresponding outer surface of each desired cylinder so that, on the one hand, all traces of ink can be removed and, on the other hand, a reactive erasing of ink-conducting layers including filling materials from a gravure printing-form cylinder is possible.