The invention relates to thermoplastic molding compositions, comprising A) from 35 to 95% by weight of at least one graft copolymer A), which is obtainable via reaction of A1) from 5 to 95% by weight of a polymer A1), which is obtained from at least one dicarboxylic anhydride a11) and from at least one vinylaromatic comonomer a12), and A2) from 5 to 95% by weight of a polyamide A2), B) from 5 to 40% by weight of at least one ungrafted or grafted, non-particulate rubber without core-shell structure B), which has functional groups which can react with the end groups of component A), C) from 0 to 50% by weight of at least one particulate or fibrous filler or particulate or fibrous reinforcing material C), D) from 0 to 60% by weight of at least one copolymer D) composed of vinyl aromatic monomers d1) and of comonomers d2), and E) from 0 to 40% by weight of at least one other additive E), where the entirety of components A) to E) gives 100% by weight, and also to processes for preparation of the thermoplastic molding compositions, to the use of the thermoplastic molding compositions for production of moldings, of foils, of fibers, or of foams, and finally to the moldings, foils, fibers, and foams obtainable from the thermoplastic molding compositions.