A device for driving a cylinder (1) of a printing machine has an electric motor (3) whose rotor (14) is arranged coaxially with respect to the cylinder (1) and is firmly connected so as to rotate with the latter, and whose stator (15) is held on a frame construction (2) in which the cylinder (1) is mounted such that it can be displaced axially. The rotor (14) and the stator (15) are dimensioned and coupled to the cylinder (1) and the frame construction (2), respectively, in such a way that during any axial displacement of the cylinder (1) possible during the operation of the printing machine, the gap (16) formed between stator (15) and rotor (14) remains constant both with regard to gap width (s) and with regard to length.