The present invention is directed to composite structures by thermoplastically shaping an assembly of at least two flat thermoplastically formable plastic materials placed in layers one above the other and optionally at least one upper, lower and/or intermediate layer containing a reinforcing or filler material under such conditions of temperature and pressure that shaping is accompanied by intimate union of the individual layers of the assembly, characterized in that at least one of the flat plastic materials is based on a polyisocyanate polyaddition product having a density of at least 0.8 g/cm.sup.3 which has been prepared by the reaction of(a) aromatic polyisocyanates,(b) compounds having a molecular weight of 1800 to about 12000 and containing a statistical average of at least 2.5 isocyanate-reactive groups, optionally(c) diamines in the molecular weight range of 108 to 400 containing two primary and/or secondary aromatically bound amino groups, and optionally(d) (cyclo)alkanepolyols and/or (cyclo)alkanepolyamines in the molecular weight range of 60 to 1799 optionally containing ether groups,by a single stage or multi-stage process at an isocyanate index of 60 to 140, wherein at least one of components (c) or (d) is used in a quantity such that the total quantity of components (c) and (d) is at least 5% by weight, based on the weight of component (b).