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A simple statistical segmental approach to speech pattern modelling, based on segmental hidden Markov models, is proposed which addresses some of the limitations of conventional hidden Markov model based methods. The most important features of the new approach are the use of an underlying semi-Markov process to model speech at the segment level, rather than time-synchronous frame level, and to enable improved segment duration modelling, and the development of a segment model in which separate statistical processes are used to characterise extra-state and intrastate variability, thus making the temporal independence assumption more acceptable within a segment. A basic mathematical analysis of gaussian segmental hidden Markov models is presented and model parameter re- estimation equations are derived. The relationship between the new type of model and variable frame rate analysis and conventional gaussian mixture based hidden Markov models is exposed.