An engine supplied with compressed air, or with any other compressed gas contained in a high-pressure storage tank and comprising: - at least one main drive piston which slides in a drive cylinder driving a crankshaft in a conventional connecting rod/crank arrangement, - and at least one active expansion chamber which consists of a variable volume equipped with means allowing work to be produced and which is connected, by a passage, with the volume, called dead volume, contained in the driving cylinder above the driving piston at its top dead centre, wherein: - the engine comprises an inlet duct which opens in the active expansion chamber and which allows the engine to be supplied with compressed air or with compressed gas, - the compressed air or gas is let into the expansion chamber when this chamber is at its smallest volume and which, under the thrust of the compressed air, will increase in volume, thereby producing a work, - when the expansion chamber is more or less at its maximum volume and the driving piston is more or less at its top dead centre, the inlet duct is shuttered, and the said active expansion chamber is placed in communication with the driving cylinder and the compressed air, or the compressed gas, which is contained in the active expansion chamber expands, thus pushing the driving piston back in its downstroke, thereby in its turn supplying a work, 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, characterized: - in that said passage comprises a shutter thus allowing said active expansion chamber to be isolated from or to be placed in contact with the dead volume and - in that during the expansion, the volume of the active expansion chamber is returned to its minimum volume to allow a new cycle to commence. - at least one main drive piston which slides in a drive cylinder driving a crankshaft in a conventional connecting rod/crank arrangement, - and at least one active expansion chamber which consists of a variable volume equipped with means allowing work to be produced and which is connected, by a passage, with the volume, called dead volume, contained in the driving cylinder above the driving piston at its top dead centre, wherein: - the engine comprises an inlet duct which opens in the active expansion chamber and which allows the engine to be supplied with compressed air or with compressed gas, - the compressed air or gas is let into the expansion chamber when this chamber is at its smallest volume and which, under the thrust of the compressed air, will increase in volume, thereby producing a work, - when the expansion chamber is more or less at its maximum volume and the driving piston is more or less at its top dead centre, the inlet duct is shuttered, and the said active expansion chamber is placed in communication with the driving cylinder and the compressed air, or the compressed gas, which is contained in the active expansion chamber expands, thus pushing the driving piston back in its downstroke, thereby in its turn supplying a work, * 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, characterized: - in that said passage comprises a shutter thus allowing said active expansion chamber to be isolated from or to be placed in contact with the dead volume and - in that during the expansion, the volume of the active expansion chamber is returned to its minimum volume to allow a new cycle to commence. - in that said passage comprises a shutter thus allowing said active expansion chamber to be isolated from or to be placed in contact with the dead volume and - in that during the expansion, the volume of the active expansion chamber is returned to its minimum volume to allow a new cycle to commence.