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This paper focuses on adaptive control of nonaffine nonlinear systems with zero dynamics using multilayer neural networks. Through neural network approximation, state feedback control is firstly investigated for nonaffine single-input-single-output (SISO) systems. By using a high gain observer to reconstruct the system states, an extension is made to output feedback neural-network control of nonaffine systems, whose states and time derivatives of the output are unavailable. It is shown that output tracking errors converge to adjustable neighborhoods of the origin for both state feedback and output feedback control.