We discuss non-phonon mechanisms of superconductivity of Kohn-Luttinger type for different models in 3D and 2D electron systems with repulsion at low densities including Fermi-gas model, Hubbard model and Shubin-Vonsovsky model. We construct the superconductive phase-diagrams for p-wave and d-wave superconductive pairings and demonstrate the possibility to increase T-c significantly already at low density in the spin-polarized case and in the two-band situation. We also discuss briefly the high-temperature superconductivity with T-c 100K which arises in the generalized t-J model in the parameters range realistic for cuprates.
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