It is well known that cubic NLS is a completely integrable model and in particular there exist infinitely many conserved quantities associated with this equation. We shall discuss a possible approach to obtain the corresponding densities which is quite flexible and can be useful to get informations in the no completely integrable case as well (for instance to get upper bounds on the polynomial growth of high order Sobolev norms). This is a joint work with F. Planchon and N. Tzvetkov.