(57) In an improved driving system for printing units of a printing machine, the respective printing units are driven by a common drive source via a line shaft and/or by individual drive sources and position control devices provided in the respective printing units. The line shaft (4) is preferably coupled with the respective drive sources via differential reduction gears (7). The construction of the driving system is such that mount positions of plates (3) equipped on the plate drums (2) in the respective printing units can be moved to the positions where exchange of plates can be executed simultaneously in the respective printing units, and after finishment of exchange of plate, can be returned to the mechanically registered relative phases of the plate drums before execution of the exchange of plates.