The engine (1) has at least one piston (4.1-4.3) in oscillating reciprocal motion relative to its longitudinal axis (3), connected to a crankshaft (7) by a connecting rod (6.1-6.3). The cylinders (2.1-2.3) are in a casing. The pistons are periodically pressurized by a gas under pressure in the TDC region. The casing (8) containing the cylinder is in the form of a rotor which rotates about the longitudinal axis (11) of the crankshaft, possibly in the same direction (12).