In this paper, adaptive tracking control is considered for a class of general nonlinear systems using multilayer neural networks (MNNs). Firstly, the existence of an ideal implicit feedback linearization control (IFLC) is established based on implicit function theory. Then, MNNs are introduced to reconstruct this ideal IFLC to approximately realize feedback linearization. The proposed adaptive controller ensures that the system output tracks a given bounded reference signal and the tracking error converges to an epsilon-neighborhood of zero with epsilon being a small design parameter, while stability of the closed-loop system is guaranteed. The effectiveness of the proposed controller is illustrated through an application to composition control in a continuously stirred tank reactor (CSTR) system.