<p>A composite plastic molding made up of a plastic foam and having a polyurethane skin is made by heating a reactive one-component system for form a polyurethane skin and then joining the polyurethane skin to the plastic foam. The one-component system is composed of a finely divided polyisocyanate in which from 0.1 to 25 equivalent percent of the isocyanate groups have been deactivated, a polyamine and/or polyol having a molecular weight of from 400 to 8000 and optionally a chain extending agent, a catalyst and known auxiliaries and additives.</p>