Process for the purification of an aqueous stream coming from the Fischer-Tropsch reaction which comprises: —feeding said aqueous stream containing the organic by-products of the reaction to a distillation column, obtaining two output streams: —an aqueous stream (i) exiting from the column head, enriched with alcohols having from 1 to 20 carbon atoms, preferably from 1 to 9 carbon atoms, and other optional volatile compounds; an aqueous stream (ii) exiting from the column bottom, enriched with organic acids having from 1 to 10 carbon atoms, preferably from 2 to 6 carbon atoms; —subjecting said aqueous stream (ii) to an anaerobic biological treatment obtaining a purified aqueous stream (iii); wherein said anaerobic biological treatment is carried out with a hydraulic retention time lower than 15 hours, preferably ranging from 4 hours to 10 hours, more preferably ranging from 5 hours to 8 hours.