To provide a positive displacement machine to simply, rapidly, and accurately set the zero positions of a rotor and a gear wheel by a synchroresolver.

A positive displacement machine for a compressive medium is constituted as a profiled body 4, engages profiles with each other through a gear wheel system during rotation, is provided with rotors acting without contact with each other, causes each of the shafts 3 of the rotors 4 to be drive by an electric motor 6 of itself, decides the angular position of the shaft 3 by a synchroresolver 8, electronically synchronizes an electric motor 6 thereby, and has a shaft 3 provided with gear wheels 7 for synchronization during emergency. In this positive displacement machine, at least one of the gear wheels 7 is connected directly to the rotor of the synchroresolver on its shaft 3 and the two members are releasably connected to the shaft 3 integrally in one unit.