A process for continuous or discontinuous synthesis of elastomeric copolyesters from polybutylene terephthalate (PBT) and polyoxytetramethylene glycol is described in which the tetrahydrofuran (THF) obtained as a byproduct in synthesis of polybutylene terephthalate from 1,4-butanediol is rectified and then reacted by ring-opening polymerization to form polyoxytetramethylene glycol which condenses with the free or esterified carboxyl groups of PBT to form the copolyester, whereby chain termination and catalyst deactivation are accomplished by adding 1,4-butanediol without separating the catalyst.