Abstract: A rotary piston machine adapts the Stirling principle and can operate as an engine or a heat pump. Two variable volume units (1,4) have n-lobed chambers (3,6) rotatable about a common axis at a first speed. Each chamber contains an (n+1) sided piston (2,5), these being rotatable about a different common axis at a different second speed, and co-operating with the lobes to form expanding and reducing sub-chambers. The first to second speed ratio is (n+1):n.n ducts (10,11) incorporating regenerators provide intercommunication between the chambers (3,6) and are open and closed by the relative piston rotation to exchange fluid or vapour between units. Heating may be provided for one unit, the expansion unit (1), and cooling for the other, the compression unit (4), and the ducts can also incorporate heating and cooling means.