In this paper the author, with reference to his previous works on the determination of all consevative dynamical systems with n degrees of freedom, whose correspondent Hamilton-Jacobi equation is solvable by separation of variables, exposes some properties of these systems. In the general case in which they possess k (k < n) integrals linear in the momenta, he determines an easy contact transformation which transforms theabove systems in new systems with k ignorable coordinates. These last systems admit n—h integrals quadratic in the momenta, involving the energy integral, and allow to obtain the whole solution of the dynamical equations.