The attempt to improve hydrogen quality has motivated research focused solely on the design of reactors for hydrogen production, paying little interest to their modelling and much less attention to its dynamic analysis. For these main reasons, this paper is focused on the dynamic analysis of a mathematical model of an ethanol steam reformer (ESR) for producing hydrogen. This analysis differs from other nonlinear analyses since it is applied to a specific seventh-order system, while literature presents analyses for at most fourth-order systems. The nonlinear model used is based on mass balances. It is represented by partial differential equations (PDEs), which are converted into ordinary differential equations (ODEs) by the finite-differences method over the space. A general nonlinear dynamic analysis based on equilibrium points and their local stability is carried out by using these ODEs. Dynamic analysis results show that the studied reactor has a stable equilibrium point for a physical-sense range of inputs (ethanol + water), which allow to have available key criteria for the design of control strategies.