this invention provides a process for producing with industrially good efficiency a polyester having a high melting point and biodegradability . in this process , ring - opening copolymerization of a cyclic acid anhydride containing succinic anhydride as a main component with a cyclic ether containing ethylene oxide as a main component is carried out in the presence of a catalyst by introducing successively the cyclic ether into a reaction vessel containing the cyclic acid anhydride in a melting state or solution state . the rate per hour of introducing the cyclic ether is within the range of 3 to 90 parts by weight per 100 parts by weight of the cyclic acid anhydride , and the reaction vessel has an inside pressure within the range of atmospheric pressure to 50 kgf / cm 2 as a gauge pressure .