  Moser's invariant tori for a class of nonanalytic quasi integrable even
hamiltonian systems are shown to be analytic in the perturbation parameter. We
do so by exhibiting a summation rule for the divergent series (``Lindstedt
series") that formally define them. We find additional cancellations taking
place in the formal series, besides the ones already known and necessary in the
analytic case (i.e. to prove convergence of Lindtsedt algorithm for
Kolmogorov's invariant tori). The method is interpreted in terms of a non
renormalizable quantum field theory, considerably more singular than the one we
pointed out in the analytic case.
