Models of two-stage serial and parallel thermoelectric generators have been established in this paper. Low-temperature thermoelectric material bismuth telluride and medium-temperature skutterudite are employed in the models and the exhaust gas of internal combustion engine is used as heat source. The properties of the thermoelectric materials are found to be temperature dependent. The performances including the output power, conversion efficiency and exergy efficiency vary with the temperatures of the heat and cold sources, the heat transfer coefficient between the hot and cold sides. The performances are influenced by the external resistances of the serial/parallel two-stage thermoelectric generators and the single-stage thermoelectric generator. The results show that the heat source temperature plays a key role in selection of the design of a thermoelectric generator when the heat transfer coefficient is more than 400 W/m(2) K. The performances of the single-stage thermoelectric generator of thermoelectric material bismuth telluride is better than those of the two stage thermoelectric generator when the heat source temperature is less than 600 K; the maximum values of the output power and conversion efficiency of a serial two-stage thermoelectric generator are 10.9% and 12A% higher, the maximum exergy efficiency is 12.5% higher than those of the single-stage one, when the temperature of the heat source is 800 K. (C) 2014 Elsevier Ltd. All rights reserved.