A pseudo-Jahn-Teller model describing central atom distortions is prop
osed for endohedral fullerenes of the form A@C-60 where A is either a
rare gas or a metal atom. A critical (dimensionless) coupling g(c) is
found, below which the symmetric configuration is stable and above whi
ch inversion symmetry is broken. Vibronic parameters are given for sel
ected endohedral fullerenes.