Advanced nonlinear control design methods usually depend on an analytical plant model, which in many practical applications, is often inaccurate or unavailable. Neural networks are a powerful tool to enhance a dynamic model if one is available but inaccurate, or to build a system dynamic model from experimental data. Trajectory linearization control (TLC) is a nonlinear control design method, which combines nonlinear dynamic inversion and linear time-varying (LTV) feedback stabilization to achieve robust tracking control for a broad class of nonlinear dynamic systems. In this dissertation, the research goal is to develop theories and methodologies to improve the understanding and applicability of TLC for inaccurate or lack of dynamic models by using neural networks. To this end, the following research objectives have been achieved. First, rigorous stability robustness analyses of TLC subject to the regular perturbation and singular perturbation are established. Second, a continuous-time nonlinear system identification method using neural network is developed. Third, a neural network trajectory linearization control (NNTLC) design procedure with stability analysis is proposed. Fourth, an adaptive neural network trajectory linearization control (ANNTLC) scheme is presented, in which the neural network control compensates for the system uncertainty adaptively. Illustrative examples of nonlinear applications of TLC, NNTLC and ANNTLC are also presented.