PURPOSE: To obtain the subject fiber having high flame retardancy and elastic recovery comprising an elastomer having the hard segment of a copolymer of polalkylene terephthalate and a phosphorus-containing compound and the soft segment of polytetramethylene glycol.

CONSTITUTION: In the reactor, dimethyl terephthalate(DMT), an organophosphorus compound having ester-forming groups of formula I (R1, R2 are alkyl, aryl or alkoxy; X is trivalent aliphatic group) or formula II (Ar is trivalent aromatic group; E is alkylene; (m), (n) are integers the total of which is 2 to 20) and 1,4-butanediol or the like are mixed at a molar ratio of DMT/the phosphorus compound at 80/20 to effect the ester-interchange reaction in the presence of a catalyst, under a normal pressure at 210°C to form the hard segment. Then, polytetramethylene glycol of 500 to 5,000 average molecular weight is added as a soft segment and polycondensation reaction is performed at 250°C under the pressure of less than 1 Torr to give the objective flame-retardant elastic fibers.