New clustering criteria for use when a mixture of multivariate normal distributions is an appropriate model are presented. They are derived from maximum likelihood and Bayesian approaches corresponding to different assumptions about the covariance matrices of the mixture components. Two of the criteria are modifications of the determinant of the within-groups sum-of-squares criterion of Friedman and Rubin (1967, Journal of the American Statistical Association 63, 1159-1178); these criteria appear to be more sensitive to disparate cluster sizes. Two others are appropriate for different-shaped clusters. The practical aspects of these criteria, and of another one studied by Maronna and Jacovkis (1974, Biometrics 30, 499-505) for heterogeneous covariance matrices, are outlined. An example involving the separation of two types of diabetic patients from normal subjects, each group having a distinct covariance structure, is given. The results with the three criteria appropriate for different-shaped clusters were comparable to one another and preferable to those obtained with the three criteria for similar-shaped clusters. Results obtained for the example with two additional clustering procedures are presented.