The present invention relates to composite materials made of at least one composite layer of a polyurethane and of a second composite layer which is directly bonded to the first layer and which consists of a thermoplastic material that is different from the polyurethane of layer A). The polyurethane material of layer A) is characterized by a residual content of free reaction components containing ether groups of no more than 400 ppm, and preferably of no more than 100 ppm. The invention also relates to a process for the production of these composite materials and to a method of their use as materials in motor vehicles.