DETAILED DESCRIPTION OF THE INVENTION The thermoplastic elastomer composition of the invention comprises 100 parts by weight of a polyester block copolymer and 0. 05 to 20 parts by weight of a liquid diphenylmethane diisocyanate (MDI). According to the present invention, the polyester block copolymer and the liquid MDI can uniformly be mixed to give a composition having a high melt viscosity with less variation of the qualities in the production lots, and further, the product has advantageously an improved water resistance. The polyester block copolymer used in the present invention is a thermoplastic polyester block copolymer comprising a polyester segment having a high melting point and a polymer segment having a low melting point and having a molecular weight of 400 to 6,000 wherein a polymer produced from the polyester segment having a high melting point alone has a melting point of not lower than 150. degree. C. and the polymer segment having a low melting point alone has a melting or softening point of not higher than 80. degree. C. The polymer segment having a low melting point is contained in the ratio of 5 to 80 % by weight, preferably 20 to 80 % by weight, based on the whole weight of the polyester block copolymer. The polyester composing the polyester segment having a high melting point includes polyesters obtained from an aromatic dicarboxylic acid (e. g. terephthalic acid, isophthalic acid, 1,5-dinaphthalenedicarboxylic acid, 2,6-naphthalenedicarboxylic acid, 2,7-naphthalenedicarboxylic acid, bibenzoic acid, bis(p-carboxyphenyl)methane, 4,4'-sulfonyldibenzoic acid, etc. ) and a diol having a low molecular weight (e. g. ethylene glycol, propylene glycol, 1,4-butanediol, 1,5-pentamethylene glycol, 2,2-dimethyltrimethylene glycol, 1,6-hexamethylene glycol, decamethylene glycol, p-xylylene glycol, cyclohexanedimethanol, etc. ); copolyesters obtained from two or more kinds of the above aromatic dicarboxylic acids and two or more kinds of the above diols; polyesters derived from an oxyacid such as p-(
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