The raw material used in most process for the production of cyclic diesters of alpha--hydroxiacids, such as Lactide and Glycolide, is a 10% solution of Hydroxyacid. During the evacuation of the solution and condensation reaction water, the organic molecules may be damaged. The present process is characterized by the use of reactants that bring as little water as possible to the reactor. In particular, for the production of Lactide, the main reactant may be anhydrous Calcium Lactate, that will react at about room temperature, for instance, with Sulfuric Anhydride, to give a solid mixture of Lactide, Calcium Sulfate Dihydrate and Calcium Sulfate Hemihydrate. Partial dehydration of the Dihydrate under mild temperature is followed by distillation of the Lactide out of the remaining powder of Calcium Sulfate Hemihydrate, and desublimation of the Lactide. Purification of the Lactide is done in situ in the desublimator.