Abstract: In this paper, the tracking characteristics of wavelet neural networks are studied on the basis of the traits of Lebesgue partition in the Hilbert space, by using the transpositional continuity of the operator theory and the topology structure of the relatively compact set. If the wavelet function, the activation function of hidden layer, is satisfied with the corresponding properties, the wavelet neural networks can track the smooth nonlinear function in compact set with any precision. This conclusion is drawn from the view of algebraic analysis and by the compact support and integral characteristics of wavelet function. The simulation indicates that the wavelet neural network is a universal tracker to the nonlinear function.