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In this paper, we define two general classes of probability distributions, called generalized Erlang mixture (GEM) distributions and generalized gamma mixture (GGM) distributions. These families contain some classical distributions, like the exponential and the Lindley distributions, but also many other ones introduced since more or less one decade. We provide characterizations of this family by considering the probability density function, the survival function, the hazard function, the mean residual lifetime, the moments and the Laplace transform. We have proved also some closure properties satisfied by these families. To end, we consider the problem of estimating parameters through different situations.