The composition of the invention comprises, in a medium suitable for the treatment of keratin materials, and natural non-keratin or synthetic textile materials, at least one bis-(quaternary ammonium) derivatives having the formula: ##STR1## in which R1, R2, R4 and R5 are identical or different and denote lower alkyl or lower hydroxyalkyl radicals, R3 is an alkyl, cycloalkyl, alkenyl, hydroxyalkyl