A moisture-curing urethane adhesive composition of a urethane prepolymer resulting from the reaction of a mixture of a polyether diol and a polyether triol with a diisocyanate compound, and a polyurethane compound resulting from the reaction of a mixture of a polyester polyol and a polypropyleneether polyol with a hexamethylene diisocyanate compound with addition of a monoalcohol. A modified moisture-curing urethane adhesive composition of a urethane prepolymer resulting from the reaction of a mixture of a polyether diol and a polyether triol with a diisocyanate compound, a first polyurethane compound resulting from the reaction of a copolymeric polyol consisting of propylene oxide and .epsilon.-caprolactone with a hexamethylene diisocyanate compound with addition of a monoalcohol, and a second polyurethane compound resulting from the reaction of a polyester polyol with a hexamethylene diisocyanate compound with addition of a monoalcohol.