The invention provides an apparatus for the mounting and/or demounting of at least two printing sleeves outside a printing unit of a printing machine. The printing sleeves include an outer printing sleeve forming a printing surface and an inner printing sleeve providing diameter compensation between the outer printing sleeve and an impression cylinder of the printing machine. The apparatus having a reception device onto which an inner printing sleeve can be pushed for mounting the two printing sleeves. The apparatus having at least one compressed-air device for facilitating the fixing of the inner printing sleeve on the reception device and for conducting compressed air through orifices assigned to the inner printing sleeve in order thereby to make it possible for an outer printing sleeve to be pushed more easily onto the inner printing sleeve.