A methodology for dynamic neural network (DNN) observer-based output feedback control of uncertain nonlinear systems with bounded disturbances is developed. The DNN-based observer works in conjunction with a dynamic filter for state estimation using only output measurements during on-line operation. A sliding mode term is added to the DNN structure to robustly account for exogenous disturbances and reconstruction errors. Weight update laws for the DNN, based on estimation, tracking errors, and filter output are proposed which guarantee global asymptotic regulation of the estimation error. A combination of a neural network feedforward term, along with estimated state feedback and sliding mode terms yields a global asymptotic tracking result. The developed method yields the first output feedback technique simultaneously achieving global asymptotic tracking and global asymptotic estimation of unmeasurable states for the class of uncertain nonlinear systems with bounded disturbances.