Feed forward neural networks () have been shown to obtain successful results in system identification and control. are static input-output mapping schemes that can approximate a continuous function to an arbitrary degree of accuracy. A recurrent neural network (RNN) is a dynamic mapping network which is more suitable for describing dynamic systems than the NN. According to RNN structure, it can deal with time-varying input or output through its own natural temporal operation. For this ability to temporarily store information, the structure of the network is simplified. Therefore, fewer nodes are required for system identification. The combination of wavelet theory and neural networks has lead to the development of W. W are feed forward neural networks using wavelets as activation function. In W, both the position and the dilation of the wavelets are optimized besides the weights. The WNN keeps generalization approximating property of and the capability of wavelet decomposition. W combine the capability of artificial in learning processes and wavelet localization property and have high accuracy and fast learning ability. Accordingly, the concept of the wavelet neural network (WNN) has become increasingly important and can be used for identification and control of the complex nonlinear systems. On the other hand, the recurrent wavelet neural network (RWNN) combines the properties of attractor dynamics of the RNN and good performance of the WNN. The RWNN can deal with time-varying input or output through its own natural temporal operation. In RWNN structure, the mother wavelet layer is composed of internal feedback neurons to capture the dynamic response of a system. Since the proposed RWNN is a modified model of the wavelet neural network (WNN), the RWNN includes the basic ability of the WNN such as fast convergence and localization property. Besides the RWNN has a property, unlike the WNN, that the RWNN can store the past information of the network. The objective of this thesis is to introduce an on-line recurrent wavelet neural network controller (RWNNC) for single input-single output nonlinear dynamic systems. The purpose of control is to determine control signal u such that the closed loop system output can track a desirable output. The RTRL algorithm is applied to adjust the shape of wavelet functions, feedback weights and the connection weights. Since the architecture of the RWNNC model is able to preserve past states of the networks, the RWNNC model has the capability to deal with temporal problems and also the controller has the other advantages such as simple structure and Keywords: Recurrent wavelet neural network, Nonlinear systems, Real time recurrent learning, Control