A tie layer adhesive composition for multilayer structures made up of graft composition compounded with a base resin, such as linear low density polyethylene (LLDPE), and a polyethylene having long chain branching, such as low density polyethylene (LDPE), and optionally one or more additives. The graft composition can be made up of a blend of a grafted polyolefin and an olefin elastomer and/or the reaction product of a live, grafted polyolefin and an olefin elastomer.