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In this letter, we propose a new trajectory model for characterizing segmental features and their interaction based upon a general framework of hidden Markov models. Each segment, a sequence of frame vectors, is represented by a trajectory of observed vector sequences. This trajectory replaces the frame features in the segment and becomes the input of the segmental hidden Markov models (HMM's). In our approach, we adopt polynomial trajectory modeling to represent the trajectories using a new design matrix that includes transitional information on neighborhood acoustic events. To apply this trajectory to the segmental HMM, extra- and intrasegmental variations are modified to contain trajectory information. The presented model is regarded as an extension and generalization of conventional HMM, trajectory-based segmental HMM, and parametric trajectory models. The experimental results are reported on the TIMIT corpus and performance is shown to improve significantly over that of the conventional HMM.