  In this paper we define Gevrey polyanalytic classes of order N on the unit
disk D and we obtain for these classes a characteristic expansion into
N-analytic polynomials on suitable neighborhoods of D. As an application of our
main theorem, we perform for the Gevrey polyanalytic classes of order N on the
unit disk D, an analogue to E. M. Dyn'kin's theorem. We also derive, for these
classes, their characteristic degree of the best uniform approximation on D by
N-analytic polynomials.
