Abstract: An offset printing press having a plate cylinder and, as viewed in a direction of rotation of the plate cylinder, a first applicator roller assigned to a dampening unit and a second applicator roller to an inking unit, a bridge roller in contact with the first and second applicator rollers, and a roller in contact with the first applicator roller for selectively driving the first applicator roller at the circumferential speed of the plate cylinder and at a different speed, includes a drive connection of the bridge roller so formed that, when the first applicator roller is driven at a circumferential speed different from that of the plate cylinder, the bridge roller is drivable at the circumferential speed of the plate cylinder.