Processes for producing thermoplastic molding compositions, which comprise a) from 3 to 79% by weight of one or more (methyl)styrene-acrylonitrile copolymers, which have no maleic-anhydride-derived units, b) from 15 to 91% by weight of one or more polyamides, c) from 5 to 50% by weight of one or more rubbers, d) from 1 to 25% by weight of one or more compatibilizers, e) from 0 to 2% by weight of one or more low-molecular-weight compounds which comprise a dicarboxylic anhydride group, f) from 0 to 50% by weight of one or more fibrous or particulate fillers, and g) from 0 to 40% by weight of further additives, by producing a melt comprising components A, B, and C in a first step and subsequently incorporating D, Also, thermoplastic molding compositions obtainable by these processes, the use of these thermoplastic molding compositions, and moldings, fibers, and foils comprising these thermoplastic molding compositions.