Abstract: A parallel-and-external-axis rotary piston compressor includes a housing provided with an inlet and a discharge port and at least two rotors as the main and gate rotors. These are edged with screw-likely extended tooth spaces and are arranged to interengage and with their axes parallel. The tooth profiles of the main rotor are designed to be substantially convex and outside of the pitch circle and the tooth flanks of the gate rotor are designed to be substantially concave and within the pitch circle. In order to guarantee a simple and low-cost manufacture, a robust design and small clearances both for the main and the gate rotors, with a low wear during operation, both flanks of the main rotor teeth are surfaces conforming to the envelope of a helical plane inclined with respect to the axis of the helix and which follow a constant curve course continuously from the tooth root to the tooth crest.