A valve system for internal combustion engines that is controlled by a camshaft is a potential source of engine damage if the timing thereof is disrupted (e.g. when the timing belts rupture). Furthermore, valves in combination with the camshaft and the timing chain contribute to noise and vibrations during operation. The production costs can be high. Thus, the engine is positioned higher and is heavier. Thus, there is proposed a valve mechanism composed of a plurality of gas exchange valves that revolve slowly about the cylinder wall. Each rotary valve is controlled separately and has symmetrical openings. The number of openings in the rotary valve corresponds to the number of working cycles per revolution. Since each rotary valve is driven separately and as a result of the size of the openings in the valve, it is possible to obtain different phase shifts, valve overlaps and opening times.