Internal combustion engine includes a rotary oxidizing gas compressor, a constant volume combustion chamber with pneumatically controlled intake and exhaust valves and a fuel injector, and a rotary combustion gas expander. Each of the rotary compressor and rotary expander has a pair of tangential rotors dependently rotatable in a housing, one rotor having a vane and the other a notch for allowing passage of the vane, to form a fluid tight segmented annular region through which the vane moves. The respective one of the intake valve and the exhaust valve admits a mass of high pressure compressible fluid to the region through a triangular port for expansion or from the region after compression, the mass of fluid being confined in a part of the region between the vane and the surface of the notched rotor and changing in pressure because of the change in arcuate length and volume of the confined part. The respective pairs of rotors are included on the same respective shafts. Two vanes may be included on the one rotor and two notches on the other. Two vaned rotors may cooperate with one notched rotor, the vaned rotors being on separate shafts.