Filament-forming chain-branched polyesters and copolyesters with relative molecular weight of >10000 are provided obtained by condensing into the polyester-forming starting components 50-500 ppm of one or more chain-branching agents added during the polyester manufacture and having the general formula where n=2-4.They are excellently suited for high speed spinning of textile and industrial yarns with winding speeds of 2500-10000 m/min,followed by conventional drawing or texturizing processes.