A new fuzzy adaptive control is applied to solve a problem of motion control of nonholonomic vehicles with two independent wheels actuated by a differential drive. The major objective of this work is to obtain a motion control system by using a new fuzzy inference mechanism where the Lyapunov stability can be ensured. In particular the parameters of the kinematical control law are obtained using a fuzzy mechanism, where the properties of the fuzzy maps have been established to have the stability above. Due to the nonlinear map of the intelligent fuzzy inference mechanism (i.e., fuzzy rules and value of the rule), the parameters above are not constant, but, time after time, based on empirical fuzzy rules, they are updated in function of the values of the tracking errors. Since the fuzzy maps are adjusted based on the control performances, the parameters updating ensures a robustness and fast convergence of the tracking errors. Also, since the vehicle dynamics and kinematics can be completely unknown, dynamical and kinematical adaptive controllers have been added. The proposed fuzzy controller has been implemented for a real nonholonomic electrical vehicle. Therefore, system robustness and stability performance are verified through simulations and experimental studies.