A two-stage rotary vane motor is provided that is particularly efficient for use in cryogenic refrigeration systems where the mass flow rate of the drive fluid (which may be expanding cryogen gas) varies substantially. The two-stage rotary vane motor includes a housing enclosure having first and second fluid chambers, each with their own inlets for receiving pressurized cryogen, and first and second rotors rotatably mounted within the chambers by means of a shaft assembly having an output end. In operation, when the mass flow of the drive fluid is high (350 pounds per hour), fluid is admitted through the inlets of both the chambers of the housing enclosure to drive both of the rotors. However, when the mass flow of the drive fluid drops to a low level (i.e., 100 pounds per hour), expanding cryogen is admitted only through the second chamber of the housing enclosure to drive only the second rotor. An overrunning clutch may be used to engage and disengage the first rotor from the shaft assembly in coordination with the admission of drive fluid through both or only one of the housing inlets.