The duration high-order hidden Markov model (DHO-HMM) can capture the dynamic evolution of a physical system more precisely than can the first-order hidden Markov model (HMM). The relations among the DHO-HMM, high-order HMM (HOHMM), hidden semi-Markov model (HSMM), and HMM are presented and discussed. Recursive forward and backward probability functions for the partial observation sequence were derived, and were used to calculate the expected number of state transitions and to update the DHO-HMM’s parameters. Viterbi decoding and training algorithms for the DHO-HMM are also presented. Experimental results show that the proposed expectation- maximization (EM) training algorithm can obtain more reliable and accurate estimate of DHO-HMMs than the Viterbi training method. Experimental results also show that the DHO-HMM speech recognizer is superior to the HSMM and the baseline conventional HMM recognizers. In experiments, the DHO-HMM speech recognizer trained by the EM algorithm reduces recognition errors by up to 53% compared with the baseline HMM.