  The deformed quantum Calogero-Moser-Sutherland problems related to the root
systems of the contragredient Lie superalgebras are introduced. The
construction is based on the notion of the generalized root systems suggested
by V. Serganova. For the classical series a recurrent formula for the quantum
integrals is found, which implies the integrability of these problems. The
corresponding algebras of the quantum integrals are investigated, the explicit
formulas for their Poincare series for generic values of the deformation
parameter are presented.
