Abstract: In a gravure printing unit for a rotary press, a plate cylinder supplied with printing ink from a printing unit and an impression roller, which lies essentially at right angles to the plate cylinder, form a roller gap, through which, when the rotary press is running, sheet material that is to be printed is passed. The plate cylinder rotates in a specified direction opposite to that of the impression roller and its rotational movement is composed of a leading, rotating sector from the inking unit to the roller gap and a trailing rotating sector from the roller gap to the inking unit. By means of an auxiliary device, printing ink is supplied to the peripheral surface of the plate cylinder on the trailing, rotating sector with the help of a flexible ink-supplying apron which, follows the peripheral surface of the plate cylinder, forming an ink-filled peripheral gap.