  We consider the effect of strong electron-electron attraction on
superconductivity in the dilute system of the negative U-centers. They couple
to the conducting electronic states and mediate attraction between electrons.
We predict the formation of the local Cooper pairs provided attraction exceeds
a certain threshold value. The global coherent superconducting state appears
only due to the Andreev scattering between the centers at low temperatures. The
dependence of the superconducting transition temperature and the second
critical magnetic field on attraction strength is calculated.
