Process for removing sulfur compounds contained in a residual gas with recovery of said compounds in the form of sulfur, wherein a gas obtained from a residual gas containing H.sub.s S and SO.sub.2 and having a temperature lower than 160.degree. C. is subjected to a catalytic CLAUS reaction phase with deposition of sulfur on the catalyst and periodic regeneration of the sulfur-laden catalyst and cooling of the regenerated catalyst. The gas brought in contact with the CLAUS catalyst is produced by subjecting the residual gas to a hydrogenation and hydrolysis treatment to provide the sulfur compounds in the unique form of H.sub.2 S and to cooling with water separation by condensation and then to catalytic oxidation of H.sub.2 S in CLAUS stoichiometry with cooling of the gas stream obtained from the oxidation step under 160.degree. C. in order to separate the sulfur by condensation. Application to the purification of the residual gases emitted by CLAUS sulfur plants.