In C-60 compounds the frequencies of the phonon involved in the superconductive processes (intra-molecular modes with omega(ph) up to 2300 K) are comparable with the typical electronic scale (E-F = 2900 K) and thus the two dynamics cannot be treated separately (breakdown of the adiabatic hypothesis). This implies a generalization of the standard theory to include nonadiabatic effects. The strong electronic correlation in the fullerenes causes the contribution of the nonadiabatic processes to be positive with consequent increase of the effective electron-phonon (el-ph) pairing;, and of T-c. We show that the inclusion of nonadiabatic terms in the el-ph interaction is a key element for the high values of T, in fullerenes. In particular T-c as high as 100 K are shown to be compatible with moderate values of lambda less than or similar to 1. This implies that it should be possible to increase the value of lambda, and so T-c, and still have a stable system. (C) 2004 Elsevier B.V. All rights reserved.