Abstract Traditional discrete-state HMMs are not well suited for describing steadily evolving, path-following natural processes like motion capture data or speech. HMMs cannot represent incremental progress between behaviors, and sequences sampled from the models have unnatural segment durations, unsmooth transitions, and excessive rapid variation. We propose to address these problems by permitting the state variable to occupy positions between the discrete states, and present a concrete left-right model incorporating this idea. We call this intermediate-state HMMs. The state evolution remains Markovian. We describe training using the generalized EM-algorithm and present associated update formulas. An experiment shows that the intermediate-state model is capable of gradual transitions, with more natural durations and less noise in sampled sequences compared to a conventional HMM.