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For a speech recognition system based on a continuous density hidden Markov model (CDHMM), it is shown that speaker adaptation of the parameters of the CDHMM can be formulated as a Bayesian learning procedure and it can be integrated into the segmental k-means training algorithm. Some results are reported for adapting both the mean and the diagonal covariance matrix of the Gaussian state observation densities of a CDHMM. When the speaker adaptation procedure is tested on a 39-word English alpha-digit vocabulary in isolated word mode, the results indicate that the procedure achieves better performance than a speaker-independent system, when only one training token from each word is used to perform speaker adaptation. It is also shown that much better performance can be achieved when two or more training tokens are used for speaker adaptation.