The invention proposes an engine supplied with compressed air comprising a main drive piston (1) driving a crankshaft (5) and one active expansion chamber (13) of a variable volume allowing work to be produced and which is connected, by a passage (6), with the volume contained in the driving cylinder (2), characterized in that the said passage (6) comprises a shutter (7) thus allowing the said active expansion chamber to be isolated from or to be placed in contact with the dead volume, in such a manner that the engine works according to a four-phase thermodynamic cycle: an isothermal expansion without work; a transfer-slight expansion with work said to be quasi-isothermal; a polytropic expansion with work; an exhaust at ambient pressure.