Graft compositions, useful for tie-layer adhesives, are disclosed. The graft compositions comprise the reaction product of a live, grafted polyolefin and an olefin elastomer. The grafted polyolefin is first made by heating a polyolefin and an unsaturated monomer. Further reaction of the live, grafted polyolefin with an olefin elastomer provides the graft composition. Grafting efficiency is boosted dramatically by the presence of the olefin elastomer and use of the additional reaction step. The graft composition, when formulated into a tie-layer adhesive at low concentration, affords multilayer structures with good adhesion and high clarity.