Abstract: Permanently flame-resistant synthetic linear polyesters are obtained by irporating by condensation into the polyester composed of the usual dicarboxylic acid and diol units an alkylphosphine oxide of the formula ##SPC1##Wherein the radicals R to R.sub.4 represent organic radicals of which R.sub.2, R.sub.3 and Z may be substituted by 2 hydroxyl groups altogether, R.sub.2, R.sub.3 and R.sub.4 may also represent hydrogen and a is zero or a whole number of from 1 to 4. The flame-resistant polyesters are processed into shaped structures such as fibers, filaments, sheets, injection and compression molded articles characterized by good flameproofness and dyeing properties.