A printing press arrangement has a plurality of processing stations for processing sheets. The plurality of processing stations are arranged one after another in a transport direction of the sheets for in-line processing of the sheets. At least one of the processing stations is configured as a non-impact printing device. A transfer device, which is arranged upstream of the active region of the non-impact printing device, is provided for transferring the sheets from a first processing station, which is arranged upstream of the non-impact printing device, to the non-impact printing device. The transfer device aligns, in each case, at least one of the axial register and the circumferential register and the diagonal register of each of the sheets in register relative to the printing position of the non-impact printing device.