The global need to solve pollution problems has conducted automotive engineers to promote the development and the use of electric vehicle technologies. This paper focuses on the fuel cell hybrid electric vehicle which uses a proton exchange membrane fuel cell as a main source associated to hybrid storage device: lithium ion battery and ultracapacitors. A common interest in such technology is to spread out the energy flow between its different sources in order to satisfy the power demand for any requested mission. However, the challenging task stills the optimization of this split to reduce hydrogen consumption and respect, at the same time, the system limitations such as admissible limits of storage system capacities and battery current variation. An adaptive filtering-based energy management strategy is proposed in this paper to ensure an optimum distribution of the energy between the sources taking into account dynamic and energetic constraints of each device. For more performance, a fuzzy logic system is used to adapt the frequency of separation with the system state evolution. A sliding mode control is applied to control electric characteristics (voltage and currents) in the considered hybrid power supply. Simulation results, obtained under MATLAB®/SimPowerSystems® for four driving cycles are presented. The proposed strategy achieved good performances by respecting the ultracapacitors state of charge while preserving the battery lifetime under various driving missions.