The invention provides composite elements containing a thermoplastic polymer layer, adhering to a layer comprising the reaction product of a reaction mixture containing a prepolymer containing isocyanate groups produced by the reaction of at least one isocyanate and one polycarbonate polyalcohol with a functionality of 2 to 3 and a hydroxyl number of about 40 to about 400 mg KOH/g, based on the condensation of carbonates with diols and/or triols with a molecular weight of about 62 to about 3000 g/mol, the prepolymer having an isocyanate group content of about 5 to about 48%, compounds reactive with respect to isocyanates and optionally catalysts blowing agents and/or auxiliary substances and/or additives. The present invention further provides a process for the production the composite elements.