The degeneracy structure of the eigenspace of the N-particle Calogero-
Sutherland model is studied from an algebraic point of view. Suitable
operators satisfying SU(2) algebras and acting on the degenerate eigen
space are explicitly constructed for the two-particle case and then ap
propriately generalized to the N-particle model. The raising and lower
ing operators of these algebras connect the states, in a subset of the
degenerate eigenspace, with each other.