Process for processing a mixture of substances which contains predominantly or exclusively hydrocarbons which have from M to N carbon atoms and comprise sulfur-containing hydrocarbons, where - a first feed is formed using fluid of the mixture of substances and is subjected to first separation which forms a first fraction which contains predominantly or exclusively hydrocarbons having from X to Y carbon atoms and at least part of the sulfur-containing hydrocarbon present in the first feed, and - a second feed is formed using fluid of the first fraction and is subjected to a desulfurization in which the sulfur-containing hydrocarbons present in the second feed are predominantly or completely reacted and hydrocarbons having more than Y carbon atoms are formed as by-products, so that a product mixture of the desulfurization contains predominantly or exclusively hydrocarbons having from X to Y carbon atoms and the by-products, where - M is five or six, X is five or six when M is five, or is six when M is six, Y is six, seven or eight and N is greater than Y, characterized in that - a third feed is formed using fluid of the product mixture and is subjected to a second separation in a two-part distillation column which has two structurally separate column parts (31, 32) and in which a second fraction and a third fraction are formed, where the second fraction contains at least the predominant part of the by-products present in the third feed, - fluid of the third fraction is separated further in a third separation in the two-part distillation column, and - fluid of the second fraction is used in the formation of the first feed by being recirculated into the process at a point upstream of the first separation. - a first feed is formed using fluid of the mixture of substances and is subjected to first separation which forms a first fraction which contains predominantly or exclusively hydrocarbons having from X to Y carbon atoms and at least part of the sulfur-containing hydrocarbon present in the first feed, and - a second feed is formed using fluid of the first fraction and is subjected to a desulfurization in which the sulfur-containing hydrocarbons present in the second feed are predominantly or completely reacted and hydrocarbons having more than Y carbon atoms are formed as by-products, so that a product mixture of the desulfurization contains predominantly or exclusively hydrocarbons having from X to Y carbon atoms and the by-products, where - M is five or six, X is five or six when M is five, or is six when M is six, Y is six, seven or eight and N is greater than Y, - a third feed is formed using fluid of the product mixture and is subjected to a second separation in a two-part distillation column which has two structurally separate column parts (31, 32) and in which a second fraction and a third fraction are formed, where the second fraction contains at least the predominant part of the by-products present in the third feed, - fluid of the third fraction is separated further in a third separation in the two-part distillation column, and - fluid of the second fraction is used in the formation of the first feed by being recirculated into the process at a point upstream of the first separation.