Gas-liquid nucleation in partially miscible Lennard-Jones systems is studied using the density functional theory in a perturbation approach. Nucleation properties are examined in a symmetric and an asymmetric mixture. Both systems are shown to form two kinds of mixed critical nuclei in one vapor composition. Spherically symmetric clusters with a phase separated structure are found in the asymmetric mixture; these are shown to correspond to local maxima of the Gibbs free-energy surface. A classical calculation also suggests that the cylindrically symmetric clusters found in earlier studies have higher formation energies than the spherical nuclei in the same vapor.