This invention relates to an improvement in a rotary piston machine of trochoidal construction for compressing a gaseous medium having working chambers between a trochoidal piston and a housing corresponding to the coordinated outer envelope curve, said working chambers being separated from each other by radial seals in the housing, and outlet openings closed-off by means preventing backflow for discharging medium from the working chambers, the improvement comprising trough-shaped recess means in the peripheral piston surface which, in the dead center position of the piston, are positioned immediately ahead of a radial seal.