A thermoplastic molding composition comprising A) from 2 to 98.8% by weight of at least one polyester, B) from 0 to 49.9% by weight of a rubber-free copolymer different from C) and/or G) made of b 1) from 60 to 95% by weight of styrene or of substituted styrenes of the general formula Ia or a mixture of these in which R is an alkyl radical having from 1 to 8 carbon atoms or a hydrogen atom, and R 1 is an alkyl radical having from 1 to 8 carbon atoms, and n has the value 1, 2, or 3, and b 2) from 5 to 40% by weight of at least one unsaturated nitrile, C) from 1 to 49.9% by weight of one or more impact-modified graft rubbers having no olefinic double bond in the rubber phase and having a swelling index of from 6 to 60 (in toluene), measured in accordance with the method stated in the description, D) from 0.1 to 1% by weight of a compound of the formula E) from 0.1 to 1% by weight of a mixture of compounds of the formula F) from 0 to 1% by weight of a mixture of compounds of the formula or from 0 to 1% by weight of a mixture of compounds of the formula n = from 2 to 20 or from 0 to 1% by weight of a mixture of compounds of the formula: n = from 2 to 20 or from 0 to 1% by weight of a mixture of compounds of the formula n = from 2 to 20 or a mixture of these, G) from 0 to 30% by weight of a copolymer made of g 1) from 49.5 to 99.5% by weight of structural units deriving from one or more vinylaromatic monomers, g 2) from 0 to 50% by weight of structural units deriving from one or more vinyl cyanides, g 3) from 0.5 to 40% by weight of structural units deriving from one or more dicarboxylic anhydrides, and g 4) from 0 to 25% by weight of structural units deriving from other copolymerizable monomers, where each of the % by weight values for component G) is based on the total weight of the structural units deriving from components g 1, g 2, g 3, and g 4, and the total of these values is 100% by weight, and H) from 0 to 60% by weight of other additives, where the total of the percentages by weight of A) to H) gives 100%. A) from 2 to 98.8% by weight of at least one polyester, B) from 0 to 49.9% by weight of a rubber-free copolymer different from C) and/or G) made of b 1) from 60 to 95% by weight of styrene or of substituted styrenes of the general formula Ia or a mixture of these in which R is an alkyl radical having from 1 to 8 carbon atoms or a hydrogen atom, and R 1 is an alkyl radical having from 1 to 8 carbon atoms, and n has the value 1, 2, or 3, and b 2) from 5 to 40% by weight of at least one unsaturated nitrile, b 1) from 60 to 95% by weight of styrene or of substituted styrenes of the general formula Ia or a mixture of these in which R is an alkyl radical having from 1 to 8 carbon atoms or a hydrogen atom, and R 1 is an alkyl radical having from 1 to 8 carbon atoms, and n has the value 1, 2, or 3, and b 2) from 5 to 40% by weight of at least one unsaturated nitrile, C) from 1 to 49.9% by weight of one or more impact-modified graft rubbers having no olefinic double bond in the rubber phase and having a swelling index of from 6 to 60 (in toluene), measured in accordance with the method stated in the description, D) from 0.1 to 1% by weight of a compound of the formula E) from 0.1 to 1% by weight of a mixture of compounds of the formula F) from 0 to 1% by weight of a mixture of compounds of the formula or from 0 to 1% by weight of a mixture of compounds of the formula n = from 2 to 20 or from 0 to 1% by weight of a mixture of compounds of the formula: n = from 2 to 20 or from 0 to 1% by weight of a mixture of compounds of the formula n = from 2 to 20 or a mixture of these, G) from 0 to 30% by weight of a copolymer made of g 1) from 49.5 to 99.5% by weight of structural units deriving from one or more vinylaromatic monomers, g 2) from 0 to 50% by weight of structural units deriving from one or more vinyl cyanides, g 3) from 0.5 to 40% by weight of structural units deriving from one or more dicarboxylic anhydrides, and g 4) from 0 to 25% by weight of structural units deriving from other copolymerizable monomers, where each of the % by weight values for component G) is based on the total weight of the structural units deriving from components g 1, g 2, g 3, and g 4, and the total of these values is 100% by weight, and deriving from one or more vinylaromatic monomers, g 2) from 0 to 50% by weight of structural units deriving from one or more vinyl cyanides, g 3) from 0.5 to 40% by weight of structural units deriving from one or more dicarboxylic anhydrides, and g 4) from 0 to 25% by weight of structural units deriving from other copolymerizable monomers, where each of the % by weight values for component G) is based on the total weight of the structural units deriving from components g 1, g 2, g 3, and g 4, and the total of these values is 100% by weight, and H) from 0 to 60% by weight of other additives, where the total of the percentages by weight of A) to H) gives 100%.