In this work, the mathematical dynamical model of a PEMFC stack has been developed and implemented in Matlab environment. Lots of simulations have been executed in two different load conditions. Firstly with a resistive load and finally with a synchronous electrical power drive in automotive load conditions. The innovation in this field consists in the integration in PEMFC stack mathematical dynamic model of a synchronous electrical power drive one for automotive purposes. As regards the simulations with a synchronous electrical power drive, the complete mathematical model allows to evaluate the PEMFC stack performances and electrochemical efficiency. This represents a useful design tool.