Process for purifying the hydrochloric acid obtained as by-product in the synthesis of MSA, characterized in that the gaseous flow of hydrogen chloride evacuated from the top of the synthesis reactor is placed in contact in a treatment column, counter-currentwise, with a flow consisting of an aqueous solution of an acid chosen from methanesulfonic acid, hydrochloric acid or a mixture of these two acids, at a temperature of between 80 and 130.degree. C.