The engine has a casing, mounted in which is a rotor which rests in a sealing manner against the inner wall of the casing. The engine has a closure part for an air inlet opening opening into a combustion space and an outlet for combustion gases. This engine is of complicated construction. To ensure that the engine consists of a small number of simple components which very largely run true, the rotor is assigned a rotatably mounted counter-rotor which, during part of its rotation, bounds with it the combustion space and rests in a sealing manner against the casing wall. The rotor and the counter-rotor are seated in a manner fixed in terms of rotation on shafts mounted fixed relative to the casing. The rotor has only to be rotated about its axis and bounds the combustion space with the counter-rotor and the inner wall of the casing. The rotating parts provide perfect truth of running. The engine is suitable for extremely high speeds and has a high power.