An inking system of a printing press is utilized for inking a printing cylinder. The inking system is configured as a long roller inking system and includes two distributing cylinders that are disposed serially in a roller train. A first one of these distributing cylinders is mounted, in the roller train, close to the printing cylinder. The other of these distributing cylinders is mounted, again in the roller train, further away from the printing cylinder. The printing cylinder is rotationally force-driven by an angle position controlled drive motor. One of the two distributing cylinders of the inking system is rotationally force-driven by a drive motor that is mechanically independent of the drive for the printing cylinder. The other one of the two distributing cylinders is rotationally driven by frictional engagement with adjacent rollers or cylinders. It is thus configured without a mechanical drive connection to one of the drive motors other than the frictional engagement with the adjacent roller or cylinders which are intended to rotationally drive it.