A “TurboMotor” positive displacement rotary-piston machine comprises a casing having an annular working chamber and intake and exhaust ports, two drive shafts coaxial with the annular surface defining the working chamber and provided with rotary pistons on one end thereof and with arms on the other end thereof, a stationary central gear coaxial with the surface defining the working chamber and with the drive shafts, an output shaft concentric with the drive shafts and having an offset portion carrying a carrier and a planetary gear, the planetary gear being in mesh with the stationary central gear the carrier being pivotally connected to the arms of both drive shafts through the connecting rods. The annular working chamber of the casing communicates with the intake ports and exhaust ports and/or exit channels and entrance channels arranged sequentially and contiguously.