In this paper, we propose an adaptive neural dynamic surface control (DSC) approach with $H_{infty}$ tracking performance for full dynamics of nonlinear flight systems. It is assumed that the model uncertainties such as structured and unstrutured uncertainties, and external disturbances influence the nonlinear aircraft model. In our control system, self recurrent wavelet neural networks (SRWNNs) are used to compensate the model uncertainties of nonlinear flight systems, and an adaptive DSC technique is extended for the disturbance attenuation of nonlinear flight systems. All weights of SRWNNs are trained on-line by the smooth projection algorithm. From Lyapunov stability theorem, it is shown that $H_{infty}$ performance nom external disturbances can be obtained. Finally, we present the simulation results for a nonlinear six-degree-of-freedom F-16 aircraft model to confirm the effectiveness of the proposed control system.