  Using partial derivatives $\partial_zf$ and $\partial_{\ol z}f$, we introduce
Besov spaces of polyanalytic functions on the unit disk and on the upper
half-plane. We then prove that the dilatations of each function in polyanalytic
Besov spaces converge to the same function in norm. This opens the way for the
norm approximation of functions in polyanalytic Besov spaces by polyanalytic
polynomials.
