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This paper deals with a mathematical analysis of pump efficiencies in an internal gear and balanced vane pumps. They are commonly used in current automatic transmissions including a continuously variable transmission. For these pumps, the influence of oil temperature as well as pump-operating pressures and pump speeds is clarified by using mathematical models taking oil temperature into consideration, which are constructed on the basis of actual measured flow and torque data under various pump-operating conditions. For fuel economy in a vehicle, because the pump should be operated under conditions to obtain higher pump efficiencies, it is very important to understand the relationship between the pump efficiencies and the pump-operating conditions.