This invention relates to a process for cleaning gas, in particular hydrocarbonaceous gas such as e.g. natural gas, which is contaminated with sulfur in the form of H.sub.2S and mercaptans as well as CO.sub.2.To remove the undesired sulfur-containing substances in the form of H.sub.2S and mercaptan from crude gas, it is proposed in accordance with the invention that the crude gas is introduced into an absorption and regeneration column and washed therein, three gas streams being withdrawn from this absorption and regeneration column, a first exhaust gas stream being introduced into a Claus plant, a second sour gas stream with a low H.sub.2S concentration being introduced into another absorption plant, and a third gas stream, the valuable gas with the mercaptans, being cooled and supplied to an adsorption plant, that from this adsorption plant a cleaned valuable gas is withdrawn, and a mercaptan-containing gas stream is subjected to washing, that this concentrated mercaptan-containing gas is supplied to the Claus plant.