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Purpose -The purpose of this paper is to propose an adaptive output feedback controller using wavelet neural networks with nonlinear parameterization for unknown nonlinear systems with only system output measurement. Design/methodology/approach -An error observer is used to estimate the tracking errors through output measurement information, and the wavelet neural networks are utilized to online approximate an unknown control input by adjusting their internal parameters. Findings -The controller integrates an error observer and wavelet neural networks with nonlinear parameterization into adaptive control design and is derived in accordance with implicit function and mean value theorem. The adjustment mechanism for the parameters of the wavelet neural networks can be derived by means of mean value theorem and Lyapunov theorem, and the stability of the closed-loop system can be guaranteed. Originality/value -This paper utilizes the nonlinear parametric wavelet neural networks with estimate state inputs to obtain the adaptive control input for nonaffine systems with only system output measurement, and the nonlinear wavelet parameters can be adjusted efficiently.