The invention relates to a rotary piston engine, in particular a rotary engine of trochoidal design, with a side disk (4) on the exhaust side and a rotary piston (6) with at least of one, and preferably three, through-flow openings (6) through which the mixture can flow axially, wherein the side disk (4) on the exhaust side has a side exhaust port (43) and the at least of one through-flow opening (60) has an asymmetric internal contour (600) at least on its exhaust side, so that when the rotary piston (6) passes over the side exhaust port (43) the said side exhaust port (43) is not in fluid communication with an internal area of the through-flow opening (60). The invention further relates to a rotary piston (6) for a rotary piston engine.