Organophilic phyllosilicates which have been prepared by treating a naturally occurring or synthetic phyllosilicate, or a mixture of such silicates, with a salt of a quaternary or other cyclic amidine compound, or with a mixture of such salts; polymeric systems, in particular thermoplastic polymers and thermosetting polymer systems, preferably epoxy resins, polyurethanes and rubbers, which comprise novel organophilic phyllosilicates, and also shapable moulding materials and finished mouldings in the form of composite materials, in particular in the form of nanocomposites.