  We consider the exactly solvable quantum mechanical systems whose
eigenfunctions are described by the multi-indexed orthogonal polynomials of
Laguerre, Jacobi, Wilson and Askey-Wilson types. Corresponding to the
recurrence relations with constant coefficients for the $M$-indexed orthogonal
polynomials, it is expected that the systems satisfy the generalized closure
relations. In fact we can verify this statement for small $M$ examples. The
generalized closure relation gives the exact Heisenberg operator solution of a
certain operator, from which the creation and annihilation operators of the
system are obtained.
