This paper deals with the problem of modeling and controlling the electric power stage of hybrid electric vehicle. The controlled system consists of a fuel cell (FC) as a main source, a supercapacitor as an auxiliary source, two DC-DC power converters, an inverter and a traction induction motor. The proposed strategy involves a multi-loop nonlinear controller designed to meet the three main control objectives: (i) a tight speed regulation in spite of torque load variations. (ii) a good regulation of the DC link voltage; and (iii) a perfect tracking of SC current to its reference. While a Lyapunov based approach is used to control the DC/DC power converters associated with the DC sources, the backstepping technique combined with the field oriented control strategy are invoked in order to control the induction motor. It is formally shown, using a theoretical analysis and simulation results, that the proposed controller meets all the objectives.