The specification describes a rotary piston compressor with a double-arcuate trochoidal casing track, with which a triangular piston, rotating on an eccentric shaft, makes constant sliding contact at its corners. Transfer flow pockets are provided via which the following working chamber already shuts off, and in the vicinity of the dead center position, is connected for a short time with the compression chamber coming in front of it. The transfer flow recesses are provided in at least one side part of the compressor, extend under its housing casing and extend so far inwards radially in its side wall that they are not swept by the sealing strip. Their timing edge, lying to the fore in the direction of rotation of the piston, is determined by the position of the preceding piston corner of the chamber located in the dead center position. Their timing edge, which is to the rear in the direction of rotation of the piston, is determined by the position of the same piston corner at the time of uncovering the inlet port following this preceding chamber.