A cleaning device for cleaning blocks clamped on a rotationally driven printing cylinder of a printing machine, the cleaning device including a rotatable cleaning roller, cleaning organs disposed on a periphery of the cleaning roller and which can be placed in contact with a peripheral surface of a printing cylinder, with angular positions of the cleaning organs varying in an axial direction of the cleaning roller, and the cleaning organs, in each angular position, are disposed on the periphery of the cleaning roller in only a single axial section of the cleaning roller, and control equipment for locking the cleaning organs in different angular positions.