Polyurethane foams are made and attached to a substrate having an open cavity, but reacting a polyisocyanate component and a polyol component in the presence of a blowing agent. The polyisocyanate component includes at least one isocyanate-terminated, oxazolidone-containing intermediate. This process allows for very fast curing, good quality, adherent foams to be produced on, for example, vehicle parts and assemblies, for acoustical or vibration dampening and for structural reinforcement.