The stability of symmetric and anti-symmetric localized modes in the c
ase of ''hard'' anharmonicity is considered. In the high-frequency lim
it the infinite chain is replaced by a ring of four particles. The sol
utions of this system and their stability are found analytically and t
heir relation to intrinsic localized modes are considered. The applica
bility of results and the relation between localized modes and soliton
s are also discussed.