Abstract: The invention relates to a process for flameproofing organic synthetic fibre material, wherein (a) a flameproofing agent which contains at least one bromine-containing, aromatic, aliphatic or cycloaliphatic compound and (b) a stabilizer which contains at least one organo-tin compound of tetravalent tin are applied to the fibre material and the fibre material treated in this way is subjected to a heat treatment.The process according to the invention can be carried out as a single-stage or two-stage process and yields flame-resistant fiber finishes stabilized to light and heat.