An inking device of a printing unit includes an ink reservoir, an ink film pick-up roller which has a shaft, and an inking roller having a shaft.A detector detects the distance between the inking roller and the pick-up roller and/or an angular displacement of the two shafts relative to each other and providing an output signal which represents this distance and/or this angular displacement. A controller angularly the second shaft relative to the first shaft, and the controller is capable of reducing the angular displacement and of positioning the pick-up roller in accordance with the output signal.