  Given a first order dynamical system possessing a commutative algebra of
dynamical symmetries, we show that, under certain conditions, there exists a
Poisson structure on an open neighbourhood of its regular (not necessarily
compact) invariant manifold which makes this dynamical system into a partially
integrable Hamiltonian system. This Poisson structure is by no means unique.
Bi-Hamiltonian partially integrable systems are described in some detail. As an
outcome, we state the conditions of quasi-periodic stability (the KAM theorem)
for partially integrable Hamiltonian systems.
