Based on wavelet neural networks (WNNs) and recurrent neural networks (RNNs), a class of models on recurrent wavelet neural networks (RWNNs) is proposed. The new networks possess the advantages of WNNs and RNNs. In this paper, asymptotic stability of RWNNs is researched according to the Lyapunov theorem, and some theorems and formulae are given. The simulation results show the excellent performance of the networks in nonlinear dynamic system recognition.