In this paper, a modified adaptive backstepping design procedure is proposed for a class of nonlinear systems with three types of uncertainty : (i) unknown parameters; (ii) uncertain nonlinearities and (iii) unmodeled dynamics. Nonlinear damping terms are used to counteract the uncertain nonlinear functions and a dynamic signal is introduced to dominate the dynamic disturbance. The derived adaptive controller guarantees the global boundedness property for all signals and states and at the same time, steers the output to a small neighborhood of the origin. Incidentally an adaptive output-feedback control problem is solved.