PURPOSE: To obtain easily the titled fibers having improved unwinding property and elastic recoverey, by melt spinning a block copolymer consisting of ethylene terephthalate as a hard component and a poly(oxyalkylene)terephthalate as a soft component under specific conditions.

CONSTITUTION: A polyether ester block copolymer consisting of a hard component consisting of terephthalic acid as a main acid component and ethylene glycol as a main glycol component and a soft component consisting of terephthalic acid as a main acid component and a poly(oxyalkylene)glycol as a main glycol component at (50/50)W(80/20)weight ratio between the soft and hard components is melted and extruded through a spinneret, and the extruded filaments are cooled, solidified and taken off at ≥2,000m/min speed to give the aimed elastomer fibers.