  Finite-dimensional spaces which are invariant under the action of the
Hamiltonian of the BC_N Inozemtsev model are introduced, and it is shown that
higher commuting operators also preserve the finite-dimensional spaces. The
relationship between the finite-dimensional spaces of the BC_N Inozemtsev
models and the theta-type invariant spaces of the BC_N Ruijsenaars models is
clarified. The degeneration of the BC_N Inozemtsev models and the
correspondence of their invariant spaces are considered.
