PROBLEM TO BE SOLVED: To provide a hair bleaching or hair dye composition which is excellent in finger combing at the time of shampoo, can make the glossy and good settlement hair, and further is excellent in sustainability of their effects.SOLUTION: A hair bleaching or hair dye composition contains the following component (A) and (B). Component (A): a cationic polymer having a charge density of 5.0-7.0 meq/g. Component (B): an anionic polysaccharide derivative in which a part of H of -OH in a polysaccharide compound having a constitutional unit of a formula (1) is substituted by group-(CH2)mCOO- (m is an integer of 1-5) with average degrees of substitution of 0.5-2.0 per constitutional unit, a part of H of the remaining -OH may be substituted by the alkyl group and/or alkylene group of C1-40, and the viscosity of a 2 mass% of aqueous solution (25°C) is 0.5-800 mPa s. [R' is an alkylene group of C2-4 which may be substituted by -OH respectively; n is a number of 0-10 in an average addition mole number of R'O per constitutional unit.]COPYRIGHT: (C)2015,JPO&INPIT【課題】洗髪時の指通りに優れ、ツヤのあるまとまりの良い髪に仕上げることができ、更にはそれらの効果の持続性にも優れる脱色又は染毛剤組成物の提供。【解決手段】成分(A)電荷密度5.0~7.0meq/gのカチオン性ポリマーと、成分(B)式(1)の構成単位を有する多糖化合物の-OHのHの一部が、基-(CH2)mCOO-(mは1~5の整数)によって構成単位当たりの平均置換度0.5~2.0で置換されており、残りの-OHのHの一部がC1-40のアルキル基及び/又はアルキレン基で置換されていてもよく、2質量%水溶液(25℃)の粘度が0.5~800mPa・sであるアニオン性多糖誘導体と、を含有する脱色又は染毛剤組成物。〔R'は各々-OHで置換されてよいC2-4のアルキレン基;nは構成単位当たりのR'Oの平均付加モル数が0~10となる数〕【選択図】なし