  The rings of quantum integrals of the generalized Calogero-Moser systems
related to the deformed root systems ${\cal A}_n(m)$ and ${\cal C}_n(m,l)$ with
integer multiplicities and corresponding algebras of quasi-invariants are
investigated. In particular, it is shown that these algebras are finitely
generated and free as the modules over certain polynomial subalgebras
(Cohen-Macaulay property). The proof follows the scheme proposed by Etingof and
Ginzburg in the Coxeter case. For two-dimensional systems the corresponding
Poincare series and the deformed $m$-harmonic polynomials are explicitly
computed.
