  Integrability, one of the classic issues in galactic dynamics and in general
in celestial mechanics, is here revisited in a Riemannian geometric framework,
where newtonian motions are seen as geodesics of suitable ``mechanical''
manifolds. The existence of constants of motion that entail integrability is
associated with the existence of Killing tensor fields on the mechanical
manifolds. Such tensor fields correspond to hidden symmetries of non-Noetherian
kind. Explicit expressions for Killing tensor fields are given for the N=2 Toda
model, and for a modified Henon-Heiles model, recovering the already known
analytic expressions of the second conserved quantity besides energy for each
model respectively.
