An inking unit of a printing unit and a device for printing on hollow bodies each have a cylindrical lateral surface. The device comprises the inking unit. The inking unit has an anilox roller which receives a printing ink from an ink reservoir and has an inking roller placed against a printing cylinder of the printing unit. A rider roller is arranged axially parallel to the anilox roller in a region between the ink reservoir and the inking roller, that region being located subsequent to the ink reservoir in a direction of rotation of the anilox roller. The ink reservoir interacts with the anilox roller. The rider roller is placed against the anilox roller. The rider roller is rotationally driven by the anilox roller by friction. The inking roller is rotationally driven by the anilox roller by friction. The plate cylinder and the anilox roller are each independently rotationally driven by a motor.