Fuel cell vehicles, (FCV) are characterized by the utilization on the same electric bus of an hydrogen fuel cell (FC) as a primary energy source and of storage elements like batteries as a secondary source. In our project, the fuel cell is a Polymer Electrolyte Membrane (PEM), which is well adapted for transport field applications. A Lithium rechargeable battery, more specifically a LiFePO4, is used to supplement the FC over the driving cycle. According to the requirements of the drive cycle of the vehicle, a 30 kW PEM FC system and a 4.5 kWh LiFePO4 battery is considered here.To define the power supplied by each source an energy management system is used. Two different strategies were applied in order to obtain an optimal behavior for the vehicle in terms of hydrogen consumption and considering the constraints of the system (State of Charge of the Battery): (1) a Rule based method to define the power split between the sources; (2) a dynamic programming using the graph theory to define the hydrogen optimal consumption path during the drive cycle.