  We show that the existence of algebraic forms of exactly-solvable $A-B-C-D$
and $G_2, F_4$ Olshanetsky-Perelomov Hamiltonians allow to develop the {\it
algebraic} perturbation theory, where corrections are computed by pure
algebraic means. A classification of perturbations leading to such a
perturbation theory based on representation theory of Lie algebras is given. In
particular, this scheme admits an explicit study of anharmonic many-body
problems. Some examples are presented.
