The invention relates to processes for producing thermoplastic molding compositions, where the thermoplastic molding compositions comprise a) as component A, from 3 to 79% by weight of one or more (methyl)styrene-acrylonitrile copolymers, which have no maleic-anhydride-derived units. b) as component B, from 15 to 91% by weight of one or more polyamides, c) as component C, from 5 to 50% by weight of one or more rubbers, d) as component D, from 1 to 25% by weight of one or more compatibilizers, e) as component E, from 0 to 2% by weight of one or more low-molecular-weight compounds which comprise a dicarboxylic anhydride group, f) as component F, from 0 to 50% by weight of one or more fibrous or particulate fillers, and g) as component G, from 0 to 40% by weight of further additives, where each of the % by weight values is based on the total weight of components A to G, and these give a total of 100% by weight, via mixing of components A to G in the melt, which comprises producing a melt comprising components A, B, and C in a first step of the process, in the absence of component D, and delaying the mixing to incorporate component D into this melt until a subsequent second step of the process, and also to thermoplastic molding compositions obtainable by these processes, the use of these thermoplastic molding compositions, and also moldings, fibers, and foils comprising these thermoplastic molding compositions.