Abstract: A hybrid propulsion system includes a wave rotor combustion engine operating in parallel with an electrical motor-generator element. The motor-generator element is coupled to the turbine shaft to selectively drive or be driven by the turbine shaft. In one mode of operation, the motor of the motor generator element is powered by a battery to provide rotational energy to the turbine shaft. In another mode of operation, the wave rotor combustion engine drives the generator to recharge the battery. The wave rotor combustion engine may be further directly coupled to auxiliary components without a gearbox to drive the components at substantially the same speed as the turbine shaft. The turbine rotor of the combustion engine includes a plurality of chambers defined by circumferentially spaced curved vanes that improves specific fuel consumption for the engine.