Thermoplastic moulding compositions comprising: A) from 40 to 96% by weight of a partly aromatic polyamide, B) from 2 to 30% by weight of a copolymer of B1) from 35 to 89.9% by weight of ethylene, B2) from 10 to 60% by weight of 1-octene or 1-butene or propylene or a mixture thereof and B3) from 0.05 to 5% by weight of functional monomers selected from the group consisting of carboxylic acid, carboxylic anhydride, carboxylic ester, carboxamide, carboximide, amino, hydroxyl, epoxide, urethane and oxazoline groups and mixtures thereof, C) from 1 to 50% by weight of fibrous or particulate fillers or mixtures thereof, D) from 0.1 to 10% by weight of D1) at least one highly branched or hyperbranched polycarbonate having an OH number of from 1 to 600 mg of KOH/g of polycarbonate (in accordance with DIN 53240, Part 2) or D2) at least one highly branched or hyperbranched polyester of the AxBy type where x is at least 1.1 and y is at least 2.1 or a mixture thereof, E) from 0 to 15% by weight of an electrically conductive additive, F) from 0 to 30% by weight of further additives, where the sum of the percentages by weight of the components A) to F) is 100%.