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This paper presents a design methodology for stable predictive control of nonlinear discrete-time systems via recurrent wavelet neural networks (RWNNs). This type of controller has its simplicity in parallelism to conventional generalized predictive control design and efficiency to deal with complex nonlinear dynamics. A mathematical model using RWNN is constructed, and a learning algorithm adopting a recursive least squares is employed to identify the unknown parameters in the consequent part of the RWNN. The proposed control law is derived based on the minimization of a modified predictive performance criterion. Two theorems are presented for the conditions of the stability analysis and steady-state performance of the closed-loop systems. Numerical simulations reveal that the proposed control gives satisfactory tracking and disturbance rejection performances. Experimental results for position control of a positioning mechanism show the efficacy of the proposed method with setpoint changes.