Abstract: A rotary piston machine is shown that is operable with a compressible fluid; such as a rotary pump, compressor or engine construction. There is a housing having an inner and an outer ring member that are rotatably mounted on a common axis. The outer ring has at least two diametrically opposed inwardly directed segmental pistons. The inner ring has at least two diametrically opposed outwardly directed segmental pistons so as to define working chambers therebetween. An oscillating coupling means is positioned within the inner ring and flexibly joined to both ring members as well as rotating around a fixed offset crankpin to cause the inner and outer pistons to change position with relation to each other as the two ring members revolve around their common axis so as to create compression and expansion strokes.