Delamination-resistant heat-shrinkable multilayer oxygen barrier film containing polyester

A first multilayer shrink film has an outer polyester layer, an inner 02-barrier layer, and a tie layer between the polyester layer and the barrier layer. A second multilayer film an outer polyester layer, an inner polyamide layer, and a tie layer between the polyester and polyamide layers. The tie layer comprises a styrene-based polymer, and the tie layer in the second film comprises an anhydride functional styrene based copolymer. Included are a packaging article comprising the film, a packaging process utilizing the film, a process for making the film, and a packaged product comprising a packaging article made the film, with a product inside the package.