[en] The formation and the structure of a mixed quark-nucleon phase in neutron star cores are studied, for different models of the nuclear symmetry energy. Simple parametrizations of the nuclear matter equation of state and the bag model for the quark phase are used. For lower values of the bag constant B the properties of the mixed phase do not depend strongly on the symmetry energy. For larger B we find that a critical pressure for the first quark droplets to form in the nucleon medium is strongly dependent on the nuclear symmetry energy, but the pressure at which last nucleons disappear is independent of it. (author)