A device for pressing on a flexible printing form when it is being pulled onto a form cylinder of an offset printing press. The device makes it possible to use an offset cylinder which is not in phase. The device for pressing on a flexible printing form when it is being pulled onto a form cylinder of an offset printing press, has a switching-on or switching-off apparatus of an offset cylinder with respect to the axially parallel form cylinder and an axially parallel impression cylinder, the offset cylinder having a channel, above which a cover is arranged, and the impression cylinder having a gripper system for sheets. The gripper system protrudes beyond the circumferential contour of the impression cylinder and dips into the channel of the offset cylinder during printing. The surface of the cover has support surfaces for the printing form which supplement the contour of the offset cylinder, and the cover has cutouts or depressions which lie deeper and in the circumferential direction to allow the gripper system to dip into.