A polyurethane adhesive which is useful in bonding porous and non-porous surfaces is provided. The adhesive is especially useful in bonding windshield glass into automotive frames under a variety of environmental conditions, particularly in after market windshield replacement applications. The polyurethane includes at least one urethane prepolymer which is based on at least one thermoplastic polyol. In one embodiment, the urethane prepolymer may be formed from one or more polyisocyanates, one or more polyetherpolyols and one or more thermoplastic polyesterpolyols, wherein the prepolymer has a free isocyanate content of from about 0.6 to about 3.5% by weight, based on the weight of the polyurethane. In another embodiment, a one-part adhesive composition is provided which includes an isocyanate-functional and thermoplastic polyurethane prepolymer having a free isocyanate content of from about 0.6 to about 3.5% by weight, based on the weight of the polyurethane, and a combination of several catalysts which are capable of catalyzing the reaction of isocyanate moieties with isocyanate-reactive moieties while providing less temperature dependent catalyzing of the reaction between isocyanate moieties and water. Also provided is a process for bonding two or more substrates together utilizing the polyurethane adhesive. In automotive windshield replacement applications, the polyurethane adhesive allows for a sufficient working time and development of green strength to provide a safe drive-away time within 1 hour at a temperature from about 0 to about 100° C.