An external axis rotary piston compressor having a housing formed with at least two overlapping, parallel-axis cylindrical inner chambers each having a shaft passing therethrough. On the one shaft there is a cylindrical working rotor forming an annular working chamber with the housing wall surrounding the same, and including a shutoff tooth or projection. On the other shaft, which rotates counter thereto, there is provided a cylindrical shutoff rotor which runs along the housing wall and rides on the working rotor; this shutoff rotor includes a recess for engagement-free passage of the shutoff tooth or projection therethrough. The body of the working rotor is a hollow cylinder; when the hollow cylinder rotates, a port or control opening provided in the shutoff tooth or projection coincides with a further port or control opening located in a stationary sleeve arranged in the hollow cylinder, which is mounted in a first side part of the housing and is rigidly and coaxially connected with the drive shaft mounted in the other side part. An inlet opening is provided for the working gas into the suction chamber in the rearward side of the hollow shut-off tooth or projection as seen in the direction of rotation of the working rotor. An outlet passage extending essentially tangential to the direction of movement of the working rotor conveys working gas.