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An alternative adaptive scheme to achieve output tracking for nonlinear systems with parametric uncertainties is considered. The proposed approach is based upon a combination of the adaptive backstepping design method and a Sliding Mode Control (SMC) scheme to design dynamical adaptive sliding mode controllers and provide robust output tracking even in the presence of unknown disturbances. The validity of the proposed approach, regarding tracking objectives and robustness with respect to bounded stochastic perturbation inputs, is tested through digital computer simulations.