Terephthalate unsaturated copolyesters with ethylene glycol and 2-butene-1,4-diol, with ethylene glycol and 2-butyne-1,4-diol, with ethylene glycol and diethylene glycol, and with 2-butyne-1,4-diol were synthesized by trans-esterification reactions. Proton nuclear magnetic resonance spectroscopy was used to elucidate the structures of the copolyesters. The intrinsic viscosities of the copolyesters were measured in o-chlorophenol at 30°C. The number-average molecular weights of these copolyesters were determined by using a vapor pressure osmometer. The thermal behaviors of the copolyesters were studied by differential thermal analysis and are discussed in terms of structural differences.