The purpose of the present article is the study of duals of functional codes on algebraic surfaces. We give a direct geometrical description of them, using differentials. Even if this description is less trivial, it can be regarded as a natural extension to surfaces of the result asserting that the dual of a functional code $C_L(D,G)$ on a curve is the differential code $C_{\Omega }(D,G)$ . We study the parameters of such codes and state a lower bound for their minimum distance. Using this bound, one can study some examples...