Olgiati, Alessandro2017-02-162017-02-162017-02https://openscience.sissa.it/handle/1963/35272We report on a recent result concerning the effective dynamics for a mixture of Bose-Einstein condensates, a class of systems much studied in physics and receiving a large amount of attention in the recent literature in mathematical physics: for such models, the effective dynamics is described by a coupled system of nonlinear Schödinger equations. After reviewing and commenting our proof in the mean field regime from a previous paper, we collect the main details needed to obtain the rigorous derivation of the effective dynamics in the Gross-Pitaevskii scaling limit.enPreprint