Finite mixtures of linear mixed models are increasily applied in differentareas of application. They conveniently allow to account for correlations betweenobservations from the same individual and to model unobserved heterogeneity betweenindividuals at the same time. Different variants of the EM algorithm arepossible for maximum likelihood (ML) estimation. In this paper two different versionsfor fitting this model class are presented. One variant of the EM algorithmrequires weighted ML estimation. As this fitting method might not be readily availablein standard software sufficient conditions which allow to transform a weightedinto an unweighted ML estimation problem are derived.