Surface segregation in thin films of binary liquid mixtures consisting of random olefine copolymers was studied by nuclear reaction analysis over a wide temperature and composition range. A divergence of the surface excess Gamma was indicated as the binodal of each mixture was approached from the one-phase region, even at temperatures 100 degrees C below the critical point T-c, and interpreted as the advent of complete wetting behavior. A consistent description of the adsorption isotherms in terms of a mean field approach assuming a short-ranged surface potential f(s) is feasible, but requires an unexpected temperature dependence of f(s). This dependence causes the wetting transition temperature to be located lower than expected on the basis of present models.