An engine supplied with compressed air includes 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). The passage (6) includes a shutter (7) thus allowing the 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 known as quasi-isothermal; * a polytropic expansion with work; * an exhaust at ambient pressure.