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The energy transition in the field of individual transport requires first of all changes in thinking: Do we need such important mobility ranges in our everyday lifes? How to use the vehicles stopping times for battery charging?...etc. However, this energy transition also requires technological improvements, mainly in the storage of electrical energy. In this context, the electric vehicle application is a rather particular field of application since it requires both a high degree of energy and a high power requirement. It tends not to be compatible with existing storage systems. One of the ideas to overcome this problem is to use a High Energy lithium-ion battery (HE) coupled with supercapacitors. The latter is used as a buffer to assist and preserve the battery, by responding to high and medium changes of current. It can also be charged during the deceleration and braking phases. In this case, the battery only sees the slow current changes. This paper presents a modelling, identification and validation of the behavior of the two main energy storage devices, battery and supercapacitor, of the hybrid energy storage system (HESS) in electric vehicle applications. Besides of both main storage elements, the HESS includes a bi-directional DC/DC power converter suitable for power electronic interface between the battery main energy storage system and the supercapacitor. This work begins by the modeling of DC/DC converter. Then the electric state space models of both power sources, battery and supercapacitor, are also developed. And following that lead, the identification of both storage components constituting the HESS is carried out via many optimization methods based on experimental data of an urban electric vehicle. For that, a test bench is used for battery and supercapacitor characterization, while trying to be as close as possible to the real electric vehicle application. The obtained results show the good performance of the state space developed models comparing with the experimental results from a test bench developped in our laboratory at INSA Strasbourg.