A trajectory model, derived from the HMM by imposing explicit relationship between static and dynamic features, is developed and evaluated. The derived model, named 'trajectory-HMM', can alleviate some limitations of the standard HMM, which are i) piece-wise constant statistics within a state and ii) conditional independence assumption of state output probabilities, without increasing the number of model parameters. In this talk, a Viterbi-type training algorithm is also derived. This model was evaluated both in speech recognition and synthesis experiments. In speaker-dependent continuous speech recognition experiments, the trajectory-HMM achieved error reductions over the standard HMM. The experimental results of subjective listening tests shows that introduction of the trajectory-HMM can improve the quality of synthetic speech generated from HMM-based speech synthesis system which we have proposed.