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In order to develop a control strategy for hydrogen fuel cell based powertrain, the dynamic models of the fuel cell stack and its auxiliary components must be devised. All The mathematical models currently available are able to estimate the polarization curve of the fuel cell at steady state condition, based on input variables like cathode and anode pressures and cell temperature. For automotive applications, the transient behavior of the fuel cell must be considered, since the powertrain is submitted to severe variations on the electrical power consumption during normal vehicle operation. Lumped models of the air and hydrogen supply systems, as well as other subcomponents like air compressor, coolers and humidifiers allow one to have a better understanding of the fuel cell behavior during transients and steady-state operation.