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In this paper, we expand a fully recurrent wavelet neural network (FRWNN) for the multi-input multioutput (MIMO) nonlinear dynamic systems identification. The presented identifier combines the properties of recurrent neural network (RNN) such as storage of past information of the network and the basic ability of wavelet neural network (WNN) such as the fast convergence and localization properties. Here, we use the MIMO FRWNN to identify the single-input single-output (SISO) and MIMO nonlinear dynamic systems. The real time recurrent learning (RTRL) algorithm is applied to adjust the shape of wavelet functions and the connection weights of the network. The simulation results verify that the FRWNN is capable of accurately identifying nonlinear dynamic systems and can rapidly get the dynamical performance. Also in this paper, the FRWNN is compared with a fully recurrent neural network (FRNN) that the structures of both are similar. Compared to the FRNN, the FRWNN has a less error and better performance.