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The electron-phonon interaction plays a fundamental role in the superconducting and normal-state properties of all the high-Tc materials, from cuprates to fullerenes. Another common element of these compounds is in addition the extremely small Fermi energy EF, which is comparable with the range ωph of the phonon frequencies. In such a situation the adiabatic principle ωph/EF⪡1, on which the standard theory of the electron-phonon interaction and of the superconductivity relies, breaks down. In this contribution we discuss the physical consequences of the breakdown of the adiabatic assumption, with special interest on the superconducting properties. We review the microscopic derivation of the nonadiabatic theory of the electron-phonon coupling which explicitly takes into account higher-order electron-phonon scattering not included in the conventional picture. Within this context we discuss also the role of the repulsive electron-electron correlation and the specific phenomenology of cuprates and fullerides

Nonadiabatic breakdown and pairing in high-Tc compounds