We analyze the microscopic origin and the physical properties of the superconducting phase recently observed in MoS 2 . We show how the combination of the valley structure of the conduction band, the density dependence of the screening of the long-range Coulomb interactions, the short-range electronic repulsion, and the relative weakness of the electron-phonon interactions makes possible the existence of a phase where the superconducting order parameter has opposite signs in different valleys, resembling the superconductivity found in the pnictides and cuprates.