Abstract: In the purification of maleic anhydride obtained with an oxidation process, by means of absorption with an organic solvent and fractionation of the resulting liquid phase and purification of the crude maleic anhydride thus separated, the above purification being accomplished through two serially placed fractionating columns, the accumulation of polymerisable acrylic acid overhead the first fractionating column of the purification section, and of water as well as of maleic acid overhead the second fractionating column of the purification section, is avoided by carrying the overhead vapours of said first fractionating column to an absorption tower, preferably operating with the same absorption organic solvent used to absorb the crude maleic anhydride from the reaction mixture, and by carrying the overhead vapours of said fractionating column of said purification section to two condensers placed in series, so that the gaseous fraction, coming out of the first condenser, is fed to said second condenser.