this invention relates to processes for producing an olefin - terminated polyester . in one of the processes which comprises reacting an olefin - terminated diester compound with a lactone in the presence of a polymerization catalyst with transesterification ability , the lactone is in a limited amount added to the reaction system . in another process which comprises reacting an olefin - terminated diester compound , a lactone compound , a cyclic acid anhydride and an epoxy compound in the presence of a polymerization catalyst with transesterification ability , the lactone , cyclic acid anhydride and epoxy compound are each in a limited amount added to the reaction system . in accordance with this invention , olefin - terminated polyesters having high terminal modification rates can be synthesized .