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The paper entitled "Efficient training algorithms for HMMs using incremental estimation" by Gotoh et al. (IEEE Trans. Speech Audio Processing, vol.6, p.539-48, Nov. 1998) investigated expectation maximization (EM) procedures that increase training speed. The claim of Gotoh et al. that these procedures are generalized EM (Dempster et al. 1977) procedures is shown to be incorrect in the present paper. We discuss why this is so, provide an example of nonmonotonic convergence to a local maximum in likelihood, and outline conditions that guarantee such convergence.