  We introduce a new approach for the study of the Problem of Iterates using
the theory on general ultradifferentiable structures developed in the last
years. Our framework generalizes many of the previous settings including the
Gevrey case and enables us, for the first time, to prove non-analytic Theorems
of Iterates for non-elliptic differential operators. In particular, by
generalizing a Theorem of Baouendi and Metivier we obtain the Theorem of
Iterates for hypoelliptic analytic operators of principal type with respect to
several non-analytic ultradifferentiable structures.
