A polyester elastomer composition comprising a polyester block copolymer and a compound having, in one molecule, not less than two functional groups capable of reacting with a terminal group of the polyester block copolymer, and showing (A) a weight loss (volatility) at 150.degree. C., 2 hours of not more than 0.4% and (B) a gelation degree (gel fraction) at 250.degree. C., 4 hours of not more than 50%; and a polyester elastomer composition comprising a polyester block copolymer, a compound having, in one molecule, not less than two functional groups capable of reacting with a terminal group of the polyester block copolymer and a chain extender heating loss percentage satisfying the formula: (W1-W2)/W1.ltoreq.0.1, and a stabilizer comprising a tertiary amine as a part of its skeleton. From such composition, an elastomer molded product having fine mechanical strength, heat resistance and resistance to hydrolysis, which shows less volatility during heating and less gel and bleed out, can be obtained.