Abstract: A flameproof, halogen-free thermoplastic molding material contains, based on the molding material consisting of A, B, C, D and E,(A) 40 to 95% by weight of a thermoplastic halogen-free aromatic polycarbonate based on a diphenol,(B) from 5 to 30% by weight of one or more halogen-free graft polymers obtained from, based on B,(b.sub.1) an elastomer (rubber), which accounts for from 40 to 80% by weight, and(b.sub.2) a graft shell on this elastomer which accounts for from 20 to 60% by weight,(C) from 5 to 50% by weight of one or more halogen-free thermoplastic copolymers consisting of, based on C, from 50 to 95% by weight of styrene, .alpha.-methylstyrene, styrene which is substituted in the nucleus, methyl methacrylate or a mixture of these, and from 50 to 5% by weight of (meth)acrylonitrile, methyl methacrylate, maleic anhydride, N-substituted maleimide or a mixture of these,(D) 1 to 25% by weight of one or more halogen-free phosphorus compounds of the formula ##STR1## where R.sup.1, R.sup.2 and R.sup.