The present invention concerns a process for enriching the aroma profile of beverages, especially beer and wine, by means of extraction, using pervaporation, of aromas from the original beverage and subsequent addition of the extracted aromas to the beverage, after total or partial dealcoholization. The original beverage (1) is fed to the membrane separation module (4) wherein the permeate side (5) is under vacuum, provided by a vacuum pump (12). The feed contacts with the membrane surface and the aromas are selectively permeated to the permeate side of the membrane, where they suffer evaporation. The vapor permeate stream (5) is condensed (10) at an appropriate temperature, which can be cryogenic. After the aroma extraction, the beverage (6) is fed to a dealcoholization unit (14) for obtaining a non-alcoholic drink (15), however depleted in aroma compounds. Finally, the extracted aromas (10) are added to the dealcoholized beverage, thus an aroma enriched product (16) being obtained without considerably increasing its alcohol content.