Abstract: In the concentric rotary pressure fluid machine which can either be an engine, motor, pump or compressor, the four identical elliptical gears (54, 54, 100, 100) actuate the relative rotary motions of two identical and coaxial rotors (60, 60') characterized by varying angular accelerations with respect to time equal in magnitude but opposite in direction. Consequently, the four arcuate variable-volume-chambers ( 1, 2, 3, 4) bounded by the arcuate rotor vanes (70, 70, 70', 70') analogous to opposed pistons of the piston-cylinder machine, and the rotor cylinders (80'), axial spacer (110), hollow cylindrical shell (20) and two transverse end plates (32, 32), functioning as cylinder block symmetrically and alternately enlarge and shrink in volumes in the prescribed manner as they revolve around their common axis.