An adaptive neural network controller is developed to achieve output-tracking of a class of nonlinear systems.The global L2 stability of the closed-loop system is established.The proposed control design overcomes the limitation of the conventional adaptive neural control design where the modeling error brought by neural networks is assumed to be bounded over a compact set.Moreover,the generalized matching conditions are also relaxed in the proposed L2 control design as the gains for the external disturbances entering the system are allowed to have unknown upper bounds.