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Support vector machines are effective tools for pattern classification and nonlinear regression problems. However, efficient training algorithms still need to be investigated. In this paper, we present a dynamic neural network based method for training the support vector machines. The neural computing scheme is designed on the basis of the dual optimization problem for training the support vector machines. The proposed neural network can be implemented by analog circuits, and has the potential to deal with a large number of sample data. We apply the proposed neural network to solve a two-variable XOR problem and a three-variable XOR problem using two different inner-product kernel functions. Simulation studies show that the proposed method is efficient for training support vector machines. Discussions on further researches are given in the paper.