Despite its crucial role in standard superconductivity, the relevance of the electron-phonon coupling in high- Tc compounds is still unclear. More generally, it is not yet understood if in the mild/strong coupling regime the electron-phonon interaction can induce strong correlations between the carriers so as to produce superconducting properties compatible with those of the new superconductors. It is the aim of the present proposal to analyze properties of strongly correlated systems and to investigate theoretically this possibility. In particular, we plan to analyze the transition between the adiabatic strong coupling regime (polaron/bipolaron formation), characterized by the nonlinear properties of the electron-phonon coupling and the antiadiabatic intermediated coupling regime, where quantum effects become relevant. In this regime the bipolaronic ground state is expected to become unstable and form a superconductive condensate state. The transition will be investigated using mathematical and computational techniques previously developed in the analysis of quantum properties of small systems where nonlinearity is dominant.