Abstract: The present invention pertains to rotary internal combustion engines and essentially relates to an engine including a body that comprises an inner cylindrical cavity as well as side covers. The cavity comprises a rotor-piston which is concentrically mounted therein, which comprises side surfaces, radial protrusions and radial recesses on its peripheral surface, and which forms together with the body a plurality of segmented cavities. The side surfaces of the rotor-piston abut tightly with the side covers, while the radial protrusions at the peripheral surface of the rotor-piston abut tightly with the inner cylindrical surface of the body cavity. The combustion chamber is located beyond the limits of the inner cylindrical cavity and communicates with the latter through inlet and outlet channels provided with controlled slide valves.