Brominated vinylaromatic-diene block copolymers (Br-SBC) comprising a vinylaromatic polymer block S and a brominated diene polymer block BB, wherein before bromination the weight-average molar mass Mw of the block S is greater than or equal to Mw of the block BB, use thereof as flame retardants, and also polymer compositions comprising these for unfoamed and foamed thermoplastic polymers, for example EPS and XPS.