PURPOSE: To obtain the subject acidic composition having excellent storage stability and high bleaching power by using hydrogen peroxide, a nonionic surfactant, a carboxylic acid-type polymer and a specific organic phosphonic acid (salt) at specific ratios.

CONSTITUTION: The objective composition having pH of 1.5-6 contains (A) 0.5-10wt.% of hydrogen peroxide, (B) 0.1-20wt.% of a nonionic surfactant, (C) 0.05-5wt.% of a carboxylic acid-type polymer and (D) 0.0001-1wt.% of an organic phosphonic acid (salt) of formula I and/or formula II [X is H or l-4C alkyl; Y is H, OH or 1-4C alkyl; M is H or alkali metal; (n) is integer of 0-5; (m) is integer of from 0 to (2n+6)].