Method for obtaining biodegradable polymers that has a stage of esterification and/or transesterification and amidation reaction, a stage of prepolycondensation, a stage of polycondensation, a stage of extraction and a stage of drying, eliminating the use of chain extenders. The polymer can achieve all the range of viscosities desired and with an improved colour compared to the polymer from other methods, where chain extenders are used, provide a more efficient process, that is environmentally cleaner and safer for the operatives.