Combustion engine having a rotor, a housing and at least two combustion chambers which are formed between the rotor and the housing, wherein the housing has at least one ignition recess on the side thereof which faces the rotor, into which ignition recess a fuel feed and ignition system opens. At least one valve device which is mounted rotatably in the housing is configured for dividing the combustion chambers at least temporarily into an ignition chamber and a compression chamber. The valve device has at least one rotor passage section, at least one closing section and at least one gas passage section. Alternatively, the valve device temporarily at the same time disconnects a compression chamber from a first combustion chamber and an ignition chamber from a second combustion chamber, wherein there is a fluidic connection during this time between the ignition chamber and the compression chamber.