A sheet-fed offset rotary printing machine is used for multicolor printing. A plate cylinder and a rubber blanket cylinder are utilized, as are first and second impression cylinders. Either of these two impression cylinders is operable with the blanket cylinder. Sheets to be printed can have a length corresponding to a nominal diameter, or to twice a nominal diameter. The first impression cylinder has a plurality of controllable gripper systems while the second impression cylinder has at least one controllable gripper system.