Method for operating a gas expansion engine by means of a gas, preferably by means of CO2, which comprises a working cylinder having at least one inlet valve and one outlet valve , and a stroke piston carrying out piston strokes between a first piston return point (UT, 14) and a second piston return point (OT, 17) in the working cylinder in a back-and-forth motion, which stroke piston delimits an expansion space and the size of the expansion space changes by means of its back-and-forth motion, wherein the method comprises a cycle consisting of at least the following steps: a) A work cycle is carried out by introducing an input volume of the gas in saturated state via the opened inlet valve into the expansion space and a motion, resulting from an expansion of the input volume , of the stroke piston is carried out, which stroke piston is moved when the expansion space increases in size in the direction of the first piston return point (14, UT), wherein b) before the first piston return point (14, UT) is reached by the stroke piston , the gas is introduced in liquefied state into the expansion space , and then c) a compacting cycle is carried out by means of a motion of the stroke piston in the direction of the second piston return point (OT, 17) by reducing the size of the expansion space and by means of compacting the input volume and the gas in the liquefied state , wherein the input volume of the gas is liquefied, d) before the second piston return point (OT, 17) is reached by the stroke piston , at least some of the gas located in the expansion space is displaced in liquefied state by the motion of the stroke piston in the direction of the second piston return point (OT, 17) out of the expansion space via the outlet valve into a depot , and then e) via a heat exchanger , an isobaric transfer of heat is carried out onto gas in liquefied state which is guided out of the depot until it vaporises and is available as a gas in saturated state, characterised in that f) the expansion of the inlet volume begins after the inlet valve is closed. a) A work cycle is carried out by introducing an input volume of the gas in saturated state via the opened inlet valve into the expansion space and a motion, resulting from an expansion of the input volume , of the stroke piston is carried out, which stroke piston is moved when the expansion space increases in size in the direction of the first piston return point (14, UT), wherein b) before the first piston return point (14, UT) is reached by the stroke piston , the gas is introduced in liquefied state into the expansion space , and then c) a compacting cycle is carried out by means of a motion of the stroke piston in the direction of the second piston return point (OT, 17) by reducing the size of the expansion space and by means of compacting the input volume and the gas in the liquefied state , wherein the input volume of the gas is liquefied, d) before the second piston return point (OT, 17) is reached by the stroke piston , at least some of the gas located in the expansion space is displaced in liquefied state by the motion of the stroke piston in the direction of the second piston return point (OT, 17) out of the expansion space via the outlet valve into a depot , and then e) via a heat exchanger , an isobaric transfer of heat is carried out onto gas in liquefied state which is guided out of the depot until it vaporises and is available as a gas in saturated state, characterised in that f) the expansion of the inlet volume begins after the inlet valve is closed. <EOS>