A non-compression engine having two or three variable volume mechanisms, an induction-displacer (1) and a combustion-expander (2) or an induction-displacer (1) and a combustion-expander (2) and an atmospheric-cooler (3). A working volume of gas is drawn into the induction-displacer, then displaced into the combustion-expander (2) at substantially constant volume passing through the regenerator (5). The gas in the combustor-expander (2) is further heated by combustion of a fuel then expanded to extract work. The gas is then displaced through the regenerator (5) into the atmospheric-cooler (3) at substantially constant volume, or exhaust from the regenerator at constant pressure. The gas is contracted in the atmospheric-cooler doing atmospheric work. Once the gas has equilibrated with the pressure of the atmosphere it is exhaust from the atmospheric-cooler (3).