For a class of single-input single-output continuous-time nonlinear systems, a multilayer neural network-based controller that feedback-linearizes the system is presented. Control action is used to achieve tracking performance for a state-feedback linearizable but unknown nonlinear system. The control structure consists of a feedback linearization portion provided by two neural networks, plus a robustifying portion that keeps the control magniture bounded. A stability proof is given in the sense of Lyapunov. It is shown that all the signals in the closed-loop system are uniformly ultimately bounded. No off-line learning phase is needed; initialization of the network weights is straightforward.