Using nuclear reaction analysis, we have measured the enrichment by one of the components at the surface of a binary mixture of random olefinic copolymers, with components of monomer structure E(1-x1)EE(x1) and E(1-x2)EE(x2). Here E and EE are the linear ethylene and branched ethylethylene groups (C4H8) and [C2H3(C2H5)], respectively, and x represents the fraction of the EE group randomly distributed on the chains. We examined 12 different couples covering a range x=0.38-0.97. The mixtures, whose thermodynamic behavior was established in our earlier paper, were cast in the form of films on both a silicon and on a gold-covered silicon surface, and were investigated in the one-phase region of the binodal in the vicinity of the critical temperature. We find that it is always the more flexible component-the one with a shorter statistical step length, corresponding to the higher ethylethylene fraction (higher x)-that is enriched at the polymer/air surface. Within our resolution neither component is enriched at the polymer/solid interface. These results show clearly that enthalpic rather than entropic factors dominate the surface potential driving the surface enrichment. For two of the mixtures we determined the excess of the surface-preferred species as a function of mixture composition along an isotherm in the one-phase region of the binodal. A consistent description of our data in terms of a mean-field model is provided by including in the surface potential a term in the mixture composition gradient at the polymer surface.