The invention relates to a rotary piston engine comprising a housing which forms an interior space, two rotary pistons which are arranged in the interior space, an inlet opening for introducing a fluid into the interior space, and an outlet opening for the fluid, which is located in the interior space on a side opposite the inlet opening. Each rotary piston comprises at least two sealing strips and at least two recesses on the outer circumference thereof, wherein the shapes of the recesses and the sealing strips are selected to engage the sealing strips of a respective rotary pistons in the recesses of the respective other rotary piston. In addition, the sealing strips are dimensioned in the radial direction to sealingly contact an inner wall of the housing. The invention also relates to a corresponding method for operating a rotary piston engine.