Abstract: The present invention relates to a method for synthesizing polyesters or copolyesters having a mean molar mass in mass MW, greater than 10000, by means of a direct polyesterification reaction between a diacid, diester, hydroxyacid, or hydroxyester and a diol, or between hydroxyacids or hydroxyesters, said method being characterized in that said polyesterification reaction is carried out at a temperature of 60 to 150° C. at atmospheric pressure in a reaction medium including at least one acidic ionic liquid consisting of an anion and a cation, the electrical charges of which balance each other out, and wherein at least the cation is a strong acid according to the Bronsted definition, or comprises a grouping that is a strong acid according to the Bronsted definition.