Theoretical considerations of the valence pi-bonding and free pi-radic
als of fullerenes have been made. These will yield various possible sy
mmetries and structures of the endohedral as well as exohedral single
and multiple metallofullerenes. Aside from C-60(I-h), C-34(C-3 sigma)
and C-28(T-d), we also consider C-33(C-3), C-56(T-d) and C-68(T-d) Suc
h valence views will provide new aspects for the opposite views of mol
ecular orbital calculations as well as for the arrangement of molecula
r works.