High impact strength thermoplastic molding compositions based on polyphenylene ether graft copolymers and polyamides and process for producing them. The compositions are distinguished by high toughness, very good phase adhesion, high solvent resistance, and high dimensional heat stability. The molding compositions contain 70 to 250 parts of a polyamide and 100 parts of a graft copolymer that is prepared by the reaction of 100 parts of a polyphenylene ether with 0.1 to 6 parts of a mixture of 10 to 50 mole-% maleic anhydride and 90 to 50 mole-% of a vinylaromatic compound. The molding compositions are used for the production of industrial items such as pipes, panels, or cases, for example.