Cleaning device for cleaning at least one nozzle surface and at least one contact surface, designed as a spacer surface, of at least one print head, the cleaning device having at least one cleaning element, the at least one cleaning element having at least one fluid supply means with at least one outlet opening for cleaning fluid, the at least one cleaning element having at least one sliding surface, the at least one cleaning element being designed to come into direct contact, by means of the at least one sliding surface, with the at least one contact surface of the at least one print head when the latter is arranged in a cleaning position, the at least one sliding surface having a greater extension in a cleaning direction than orthogonal to the cleaning direction, the cleaning direction being a direction in which the at least one cleaning element of the at least one cleaning device is movably arranged and/or is designed to move in order to carry out a cleaning step, the at least one cleaning element having at least one first fluid removal means with at least one removal opening for removing cleaning fluid and/or dirt and/or printing fluid, the at least one first fluid removal means having at least one boundary of the first fluid removal means, a projection plane being arranged orthogonal to the cleaning direction, the at least one sliding surface being projected into the projection plane, the boundary of the at least one removal opening of the at least one first fluid removal means having at least one first boundary point (61; 63) and at least one second boundary point (62; 64), which boundary points (61; 62; 63; 64), in a projection of the at least one first fluid removal means into the projection plane, are arranged on at least one boundary point (61; 62; 63; 64) of the at least one sliding surface at a shortest distance from at least one central axis of the at least one cleaning element, the central axis of the at least one cleaning element being an axis parallel to the cleaning direction which splits the at least one cleaning element into two parts, a plane spanned by the central axis and a z-direction splitting the at least one fluid supply means into two parts, a normal vector of a plane of the nozzle surface of a print head to be cleaned being parallel to the z-direction, the boundary of the at least one removal opening of the at least one first fluid removal means having at least one further boundary point (66; 67) which is at a greater distance from the plane spanned by the z-direction and the central axis than the first boundary point (61; 63) and the second boundary point (62; 64) and which is arranged between the first boundary point (61; 63) and the second boundary point (62; 64) along the extension of the first fluid removal means in the cleaning direction, the boundary of the at least one first fluid removal means being arc-shaped between the at least one first boundary point (61; 63) and the at least one second boundary point (62; 64), which are arranged one behind the other in the cleaning direction, characterized in that the boundary of the at least one first fluid removal means is designed such that, in the projection plane, all points on the at least one sliding surface orthogonal to the cleaning direction are superposed by at least one boundary point of the boundary between the first boundary point (61; 63) and the further boundary point (66; 67).