A flame retardant polymer composition consists of a) 20 60 percent by weight of a thermoplastic and/or cross-linked or cross-linkable elastomer and b) as a flame retardant agent 40 80 percent by weight either of an aluminum hydroxide with the material values specific surface according to BET 3 5 mg.sup.2/g mean grain size d.sub.50 1.0 1.5 .mu.m residual moisture 0.1 0.4% oil absorption 19 23% water absorption 0.4 0.6 ml/g or of an aluminum hydroxide with the material values specific surface according to BET 5 8 m.sup.2/g mean grain size d.sub.50 0.8 1.3 .mu.m residual moisture 0.1 0.6% oil absorption 21 25% water absorption 0.6 0.8 ml/g. A process of producing the flame retardant agent is characterised in that a filter-moist aluminum hydroxide obtained by precipitation and filtration with a mean grain size of 0.8 to 1.5 .mu.m is subjected to mill drying in a turbulent hot air stream in such a way that, while the grain distribution is largely retained, the BET surface is increased by at least 20%.