Thermoplastic molding materials containA) not less than 5% by weight of a polymer component consisting of from 50 to 100% by weight of polyphenylene ethers and from 0 to 50% by weight of a styrene polymer differing from component C),B) not less than 5% by weight of a polyester,C) not less than 0.1% by weight of a copolymer consisting ofC.sub.1) not less than 20% by weight of .alpha.-olefins of 2 to 8 carbon atoms, styrene or substituted styrenes of the general formula I ##STR1## where R and R.sup.1 is alkyl of 1 to 8 carbon atoms, hydrogen and/or halogen and n is 0, 1 or 2, or a mixture of these monomers,C.sub.2) not less than 0.5% by weight of a polymerizable monomer containing epoxide groups, and/orC.sub.3) not less than 0.05% by weight of a halobenzyl-containing polymerizable monomer having the structural unit (II) ##STR2## where X is halogen and R.sup.2 and R.sup.3 are each alkyl of 1 to 8 carbon atoms or hydrogen and n is 1, 2 or 3, and/orC.sub.4) not less than 0.05% by weight of a polymerizable monomer containing oxazoline groups, andC.sub.5) from 0 to 65% by weight of acrylonitrile, methacrylonitrile and further nonionic comonomers, andD) from 0 to 40% by weight of a rubber impact modifier.