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It is show that the proof of theorem 1 in the original paper of J. Leyva-Ramos and A.E. Pearson (ibid., vol. 40, p. 1291-4, 1995) is incomplete and that the state observer scheme results in steady-state error. Alternatively, a memoryless state observer for linear time-delay systems is provided. The original authors acknowledge that the criticism is correct, and suggest an alternative way of overcoming the problem.