Provided are a hair dye composition comprising a diamide compound (1) and a dye; and a hair bleach composition comprising the diamide compound (1) and an oxidizing agent. ##STR00001## wherein, R.sup.1: a C.sub.1-12 hydrocarbon group which may be substituted by a hydroxy and/or alkoxy group, R.sup.2: a divalent C.sub.1-5 hydrocarbon group, and R.sup.3: a divalent C.sub.1-22 hydrocarbon group.The hair dye composition or hair bleach composition according to the present invention suppresses hair damage during dyeing or bleaching, does not impair the moisture intrinsic to the hair, and provides excellent feeling upon use.