Abstract: A printing unit has a printing form cylinder, an impression cylinder opposite the printing form cylinder and at least one substrate carrier apparatus with which a printing substrate is moved through between the printing form cylinder and the impression cylinder, wherein the substrate is printed in a printing region between the two cylinders. The substrate carrier apparatus is moved linearly during a uniform rotation of the two cylinders along a linearly extending track, limited in length by a longitudinal extension of the printing unit. The substrate carrier apparatus is accelerated from a resting start position to an operating speed, to be reached upon reaching the printing region, the substrate carrier apparatus is moved at least in the printing region at constant speed, and the substrate carrier apparatus is decelerated after leaving the printing region to a resting end position on the track.