A two-part, solvent-free laminating adhesive including a Part A that is a liquid mixture of a first polyol and a hydroxyl functional acrylic polymer having a molecular weight of no greater than 15,000 g/mole, and a Part B that is an isocyanate-terminated polyurethane prepolymer. The adhesive is especially suited for making flexible laminates for use in food packaging. When adhered two polymeric film materials and in cured form, the adhesive provides substantially no contribution to the oxygen barrier properties of the laminate.