The main objective of this paper is to design an adaptive output feedback control for a class of uncertain nonlinear systems using only one Single-Hidden-Layer (SHL) Neural Networks (NN) in order to eliminate the unstructured uncertainties. The approach employs feedback linearization, coupled with an on-line NN to compensate for modelling errors. A fixed structure dynamic compensator is designed to stabilize the linearized system. A signal, comprised of a linear combination of the measured tracking error and the compensator states, is used to adapt the NN weights. The network weight adaptation rule is derived from Lyapunov stability analysis, and guarantees that the adapted weight errors and the tracking error are bounded. Numerical simulations of both nonlinear systems, Van der Pol example and tunnel diode circuit model, having full relative degree, are used to illustrate the practical potential of the proposed approach.