Thermoplastic molding compositions compriseA) from 10 to 90% by weight of at least one thermoplastic polymer,B) from 1 to 20% by weight of a polyethylene which contains carboxyl groups and has a mean molecular weight Mn (number average) of from 24,000 to 100,000 g/mol,C) from 5 to 60% by weight of a halogen-free flame retardantD) from 0 to 70% by weight of other additives and processing aids,where the total of the percentages by weight of components A) to D) is 100%