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Three methods for the identification of multivariate outliers (Rousseeuw and Van Zomeren, 1990; Becker and Gather, 1999; Filzmoser et al., 2005) are compared. They are based on the Mahalanobis distance that will be made resistant against outliers and model deviations by robust estimation of location and covariance. The comparison is made by means of a simulation study. Not only the case of multivariate normally distributed data, but also heavy tailed and asymmetric distributions will be considered. The simulations are focused on low dimensional (p = 5) and high dimensional (p = 30) data.