Fibrous materials of any kind is finished with an organic compound having fiber-finishing properties and containing one or several groups of the formula ##STR1## in which X is sulfonyl or carbonyl and A represents hydrogen or one equivalent of a mono-, bi- or trivalent metal or an ammonium group, is applied onto the fibrous material in the form of an aqueous or organo-aqueous solution or dispersion, and the fibrous material thus treated is then subjected, if necessary, to a heat treatment for the fixation of this organic compound onto the fibrous material. Organic fiber-finishing compounds containing the above-mentioned group may be for example dyestuffs, optical brighteners or compounds increasing the crease resistance.