Abstract: In a rotary internal combustion engine with a rotor housing (1, 2, 3, 19, 20) in which a rotor (4) is eccentrically supported, preferably three radial bores (11) at mutual equal angular distance are provided. In each of the bores (11) a sliding cylinder sleeve (12) is installed which is closed at its outer end which faces out towards the cylindrical inside of the rotor housing (1). The cylinder sleeve (12) is fastened rotatably at its inner, open end to the end covers (19, 20) of the rotor housing (1) such that the cylinder sleeves (12) turn concentrically about the center line (7') of the rotor housing (1) as the rotor rotates. A sliding piston (21) is arranged in each cylinder sleeve (12), said piston (21) being fastened using connections (22, 23, 24, 25) to the rotor (4) such that each piston (21) is the same distance from the center line (8') of the rotor (4) and rotates concentrically about this center line.