The multi-stage fluidized bod can be used to preheat the combustion air by recovering the waste heat from the exhaust gas from industrial furnaces. The dilute-phase fluidized bed may be formed to exclude the excessive pressure drop across the multi-stage fluidized bed. But, in this case, the solid particles do not reach to the thermal equilibrium due to relatively short residence time in each layer of fluidized bed. In this study, a theoretical analysis on the dilute phase multistage fluidized bed heat exchanger was performed. A parameter related to the degree of thermal equilibrium between gas and solid particles at the dilute-phase fluidized beds was derived. Using this parameter, a relatively simple expression was obtained for the thermal efficiencies of the multi-stage fluidized bed heat exchanger and air preheater. Copyright (C) 2001 John Wiley & Sons, Ltd.