The present invention provides new linear phosphorus- and halogen-containing flame retardant polyester additives for normally flammable polymers and coatings for normally flammable natural and synthetic films and fibers, for instance, polyester and cellulose ester films and fibers. The phosphorus- and halogen-containing polymers of the invention are water dispersible or can be rendered water-soluble. They can be prepared by reacting a phosphorus acid reactant such as phosphoric acid with at least one halogenated difunctional monomer. The water-soluble polyesters can be cross-linked to render them insoluble in water by heating together with a methylol compound.Said halogenated monomer is preferably an oxyalkylated diacid or diol and said halogen is attached either on one or more aromatic rings or on a cycloaliphatic ring. The halogenated diols useful in preparing the flame-retardant polymer additives of the invention are selected from the group consisting of at least one of the halogenated, saturated diols having the formula: ##STR1## wherein m and p are integers of 2 to 6; n and q in formulas A, C, and D are 0 or integers of 1 to 10 and integers of 1-10 in formula B; wherein in formulas A-C, X which is attached to an aromatic ring represents 1 to 4 halogen atoms; and wherein in formula D, X represents 1 to 2 halogen atoms and Z is hydrogen, a C.sub.1 -C.sub.6 alkyl radical, or phenyl.Polymer fibers and films such as those made from polyethylene terephthalate and cellulose ester fibers and films such as those prepared from cellulose acetate and cellulose triacetate, each containing a flame-retardant amount of the phosphorus- and halogen-containing flame-retardant polymer additives of the invention are resistant to loss of the polymeric flame-retardant additives of the invention during use.