Method and apparatus for printing on printing material

A method for printing on printing material (2) in a rotary printing press, the first, the printing substrate (2) in a press nip contacting printing press cylinder (11, 12) and a second press cylinder (21, 22) containing a pre-deposited on these printed image a first ink on the printing substrate (2) transmits, with an ink jet printing device (5) for applying an additional variable printed image of ink (7) onto the printing substrate (2) is provided which is characterized in that the ink jet printing device (5), the additional print image directly on an ink-free peripheral portion (4) of the second, the printing material (2) applied directly contacting the printing press cylinder (21) or the printed image from the second press cylinder (21, 22) on the printing substrate (2) transmitting the transfer cylinder (32, 33), and that a cleaning device (8) is provided which from said Tintenstrahldruckei nrichtung (5) applied additional printing image during the continuous printing operation of the printing press by the ink-free peripheral portion (4) removed.