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In the above paper by Kuntanapreeda-Fullmer (ibid., vol.7, no.3 (1996)) a training method for a neural-network control system which guarantees local closed-loop stability is proposed based on a Lyapunov function and a modified standard backpropagation training rule. In this letter, we show that the proof of Proposition 1 and the proposed stability condition as training constraints are not correct and therefore that the stability of the neural-network control system is not quite right. We suggest a modified version of the proposition with its proof and comment on another problem of the paper. In reply, Kuntanapreeda-Fullmer maintain the proof in the original paper is correct. Rather than identifying an error, they believe Park et al. have made a significant extension of the proof for application to stable online training networks.