We study the dynamics of an interface between two phases in interactio
n with a wall in the case when the evolution is dominated by surface d
iffusion. For this, we use an SOS model governed by a conservative Lan
gevin equation and suitable boundary conditions. In the partial wettin
g case, we study various scaling regimes and show oscillatory behavior
in the relaxation of the interface toward its equilibrium shape. We a
lso consider complete wetting and the structure of the precursor film.