To obtain a biodegradable polyester which retains sufficient strengths during its use and, when disposed of, decomposes in the natural environment into carbon dioxide and water without loading the environment by producing a polyester comprising specific structural units and having a specified number average mol.wt.

A biodegradable polyester comprising structural units represented by the formula (wherein R is a 0-18C alkylene) and having a number average mol.wt. of 25,000 or higher is obtd. by subjecting a dicarboxylic acid component comprising an aliph. dicarboxylic acid (e.g. oxalic, succinic. or glutaric acid) or its anhydride or a dialkyl ester, if necessary together with an arom. dicarboxylic acid or a tri or higher carboxylic acid, and cyclohexanedimethanol (1,4-cyclohexanedimethanol being the most suitable) to esterification or transesterification and subjecting the resultant oligomer to polycondensation in the presence of at least one polymn. catalyst selected from among titanium-, antimony-, tin-, zinc-, and germanium-based catalysts in an amt. of 1×10-4-1×10-2mol per mol of the dicarboxylic acid component.