Thermoplastic molding compositions comprising A) from 10 to 99.9% by weight of a thermoplastic polyamide, B) from 0.1 to 20% by weight of a terpolymer obtainable via copolymerization of (B1) from 1 to 70% by weight of at least one electron-deficient olefin, (B2) from 0 to 85% by weight of at least one olefin which, at its olefinic double bond, bears only hydrogen atoms and/or carbon atoms without electron-withdrawing substituents, and (B3) from 1 to 99% by weight of at least one alkoxyvinylsilane, C) from 0 to 50% by weight of a fibrous or particulate filler or a mixture of these, D) from 0 to 50% by weight of other additives, where the total of the percentages by weight of components A) to D) is 100%.