Substrates, particularly low surface energy substrates, can be bonded using certain solvent-free liquid polyurethane adhesives. The adhesive cures through reaction with moisture and/or an active hydrogen-containing curing agent to form a tough, strong, thermoset polymer having excellent chemical and heat resistance. The adhesive is based on a polyurethane prepolymer obtained by reacting a stoichiometric excess of at least one polyfunctional isocyanate having a functionality of less than 2.2 with at least one polyether polyol and at least one polyester polyol containing isophthalic acid moieties but relatively few if any phthalic acid or terephthalic acid moieties.