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We consider the fitting of normal or t-component mixture models to multivariate data, using maximum likelikhood via the EM algorithm. This approach requires the initial specification of an initial estimate of the vector of unknown parameters, or equivalently of an initial classification of the data with respect to the components of the mixture model under fit. We describe an algorithm called EMMIX that automatically undertakes this fitting: including the provision of suitable initial values if not supplied by the user. The EMMIX algorithm has several options, including the option to carry out a resampling-based test for the number of components in the mixture model.