  A pseudo-Jahn-Teller model describing central atom distortions is proposed
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 which inversion symmetry
is broken. Vibronic parameters are given for selected endohedral fullerenes.
