The invention provides a polyester block copolymer composition (R) obtained by thermally-processing a polyester block copolymer composition (Q) obtained by melt-mixing 100 parts by weight of a polyester block copolymer (P) with 0.1 5 parts by weight of an epoxy compound (C) having one or more epoxy groups under an inert gas atmosphere and not less than 102.degree. C. in a solid phase, and further, at a temperature lower than a melting point of the polyester block copolymer composition (R) obtained.