In order to make handling easier, an apparatus for pulling a sleeve onto and off a printing-press cylinder has a head piece (8) having a positioning device (13) for defining the position of the head piece (8) with respect to the cylinder (1), a connecting device (14, 15) for fixing the head piece (8) to the cylinder (1), and a centering device (12) for defining the position of the sleeve (2) with respect to the head piece (8) and a deposition bar (9) for the sleeve (2), which deposition bar (9) is attached to the head piece (8).