Abstract: A flameproof linear polyester is described containing, copolymerized in the molecule, a phosphorus compound of formula: ##STR1## where R is a hydrogen atom, an alkyl group with 1 to 4 carbon atoms or a hydroxyalkyl group, and R' is a hydrogen atom, a hydroxyalkyl group or the group --(CH.sub.2 CH.sub.2 O).sub.n H, where n varies from 1 to 4. Said linear polyester is prepared by firstly forming a low molecular weight precondensate from a dicarboxylic aromatic acid (or a relative lower alkyl diester) and an alkylene glycol, and then polycondensing in the presence of said phosphorus compound, in such a quantity as to obtain a content of phosphorus (expressed as the metal) in the linear polyester of between 0.4 and 0.8% by weight. The linear polyester thus obtained can be formed into articles such as fibres, film, sheets and other articles which, besides being flameproof, possess improved dyeing characteristics.