In a rotary printing press, there is provided a device for bringing a rubber-covered cylinder into and out of engagement with at least one of a pair of cylinders consisting of an impression cylinder and a plate cylinder, the rubber-covered cylinder being mounted on a shaft, which includes a substantially circular ring turnably disposed on the shaft of the rubber-covered cylinder, the ring being spring biased in a direction towards a middle location between two circumferentially rounded bracing stops and being formed with an indentation at a section of the circumference thereof, the ring being turnable on the shaft so as to move the indented section of the circumference thereof into a position opposite one of the bracing stops for bringing the rubber-covered cylinder out of engagement with the impression cylinder, the indented section being formed as an insert channel for accommodating therein the circumferentially rounded one bracing stop, the other of the pair of bracing stops being in continual engagement with the circular circumference of the ring and being displaceable by remote control for disengaging the rubber-covered cylinder from the plate cylinder without turning the ring, the other biasing stop also forming a support location for introducing the circumferentially rounded one bracing stop into the insert channel in an operating phase wherein the rubber-covered cylinder is disengaged from the impression cylinder, as well as in an operating phase wherein the rubber-covered cylinder is disengaged from both the impression cylinder and the plate cylinder.