A printing unit includes a press unit having a forme cylinder, a transfer cylinder, an inking unit and, preferably, a damping unit. The inking unit of each press unit applies printing ink to a forme cylinder of the respective press unit in such a way that a ductor roll of an inking unit picks up printing ink kept ready in an ink fountain and applies it to the forme cylinder of the respective press unit by a film roll interacting with the ductor roll, inking unit rolls arranged downstream of the film roll, and at least one ink applicator roll rolling on the forme cylinder. Inking unit rolls driven in rotation and inking unit rolls driven in oscillation are are driven independently from one another on the drive side.