  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.
