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In this paper, a novel mixture linear dynamic model (MLDM) for speech recognition is developed and evaluated, where several linear dynamic models are combined (mixed) to represent different vocal-tract-resonance (VTR) dynamic behaviors and the mapping relationships between the VTRs and the acoustic observations. Each linear dynamic model is formulated as the state-space equations, where the VTRs target-directed property is incorporated in the state equation and a linear regression function is used for the observation equation that approximates the nonlinear mapping relationship. A version of the generalized EM algorithm is developed for learning the model parameters, where the constraint that the VTR targets change at the segmental level (rather than at the frame level) is imposed in the parameter learning and model scoring algorithms. Speech recognition experiments are carried out to evaluate the new model using the N-best re-scoring paradigm in a Switchboard task. Compared with a baseline recognizer using the triphone HMM acoustic model, the new recognizer demonstrated improved performance under several experimental conditions. The performance was shown to increase with an increased number of the mixture components in the model.