Combined service brake and spring brake cylinder for operating a service brake and a parking brake, comprising: a) a spring brake cylinder, a spring brake piston and at least one accumulator spring loading the spring brake piston in a direction of application of the parking brake, wherein the spring brake piston is displaceably guided on a radially inner circumferential surface of the spring brake cylinder, and the spring brake piston and the spring brake cylinder delimit a spring brake chamber which can be ventilated by a parking brake pressure, b) a service brake cylinder and a service brake piston, the service brake cylinder and the service brake piston delimiting a service brake chamber which can be pressurized with a service brake pressure and vented, wherein c) the service brake cylinder, viewed radially, is arranged inside the spring brake cylinder, and d) wherein the service brake piston is displaceably guided directly on a radially inner circumferential surface of the service brake cylinder, or e) wherein a diaphragm cooperating with the service brake piston is attached to the service brake cylinder and/or to the spring brake cylinder, and wherein f) between a radially outer circumferential surface of the service brake cylinder and the spring brake cylinder a spring chamber is formed as an annular chamber in which the at least one accumulator spring is arranged, characterized in that g) a breathing device is provided comprising at least: g1) a breathing valve which is arranged in a through-opening of the service brake piston and is controlled by the service brake pressure in the service brake chamber in such a way that it assumes an open position when the service brake chamber is vented, in which a first flow connection between the service brake chamber and a return spring chamber is open, and it is brought from the open position into a closed position, in which the first flow connection is blocked, when the service brake chamber is pressurized, g2) a second flow connection -between the return spring chamber and the spring chamber, g3) a third flow connection between the spring chamber and the atmosphere. a) a spring brake cylinder, a spring brake piston and at least one accumulator spring loading the spring brake piston in a direction of application of the parking brake, wherein the spring brake piston is displaceably guided on a radially inner circumferential surface of the spring brake cylinder, and the spring brake piston and the spring brake cylinder delimit a spring brake chamber which can be ventilated by a parking brake pressure, b) a service brake cylinder and a service brake piston, the service brake cylinder and the service brake piston delimiting a service brake chamber which can be pressurized with a service brake pressure and vented, wherein c) the service brake cylinder, viewed radially, is arranged inside the spring brake cylinder, and d) wherein the service brake piston is displaceably guided directly on a radially inner circumferential surface of the service brake cylinder, or e) wherein a diaphragm cooperating with the service brake piston is attached to the service brake cylinder and/or to the spring brake cylinder, and wherein f) between a radially outer circumferential surface of the service brake cylinder and the spring brake cylinder a spring chamber is formed as an annular chamber in which the at least one accumulator spring is arranged, characterized in that g) a breathing device is provided comprising at least: g1) a breathing valve which is arranged in a through-opening of the service brake piston and is controlled by the service brake pressure in the service brake chamber in such a way that it assumes an open position when the service brake chamber is vented, in which a first flow connection between the service brake chamber and a return spring chamber is open, and it is brought from the open position into a closed position, in which the first flow connection is blocked, when the service brake chamber is pressurized, g2) a second flow connection -between the return spring chamber and the spring chamber, g3) a third flow connection between the spring chamber and the atmosphere. g1) a breathing valve which is arranged in a through-opening of the service brake piston and is controlled by the service brake pressure in the service brake chamber in such a way that it assumes an open position when the service brake chamber is vented, in which a first flow connection between the service brake chamber and a return spring chamber is open, and it is brought from the open position into a closed position, in which the first flow connection is blocked, when the service brake chamber is pressurized, g2) a second flow connection -between the return spring chamber and the spring chamber, g3) a third flow connection between the spring chamber and the atmosphere.