Finite mixtures of nonparametric components represent a new and important area of statistical research. In this talk, we introduce an EM-type algorithm for estimation of these mixtures. The observations are assumed to be multidimensional. Coordinates of observations are assumed to be independent conditional on knowing which component they came from. The algorithm is designed for any number of components and any number of dimensions. As opposed to an earlier algorithm of Benaglia, Chauveau and Hunter (2009), this algorithm has an explicit objective function that it maximizes. Moreover, it also possesses a verifiable ascent property with respect to that objective function. The approach we use to construct this algorithm is based on the so-called regularization argument of Eggermont and LaRiccia, first introduced in their series of papers on *mixing density* estimation in 1990’s. We apply a similar approach to the problem of nonparametric estimation of *finite mixtures. * To the best of our knowledge, this is the first true EM-type algorithm that can fit a mixture of an arbitrary number of multivariate nonparametric components. Extensive simulations demonstrate an excellent performance of the new algorithm in a variety of situations.