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This paper presented a recurrent radial basis function network-based (RBFN-based) fuzzy neural network (FNN) to control the position of x-y table mover to track periodic reference trajectories. The two-axis motion control system was composed of two permanent-magnet linear synchronous motors (PMLSM). The proposed recurrent RBFN-based FNN combined the merits of self-constructing fuzzy neural network (SCFNN), recurrent neural network (RNN) and RBFN. The structure-learning and parameter-learning phases were performed concurrently. The structure learning was based on the partition of input space, and the parameter learning was based on the supervised gradient descent method using a delta adaptation law. The simulation results show that the designed control system of XY table has strong robustness and high contour accuracy.