A bleaching composition comprising:(a) Hydrogen peroxide or peroxide that produces hydrogen peroxide in aqueous solution; and(b) An organic acid peroxide precursor that produces organic acid peroxide by reacting with said hydrogen peroxide or peroxide that produces hydrogen peroxide in aqueous solution, wherein said organic acid peroxide is represented by general formula (I): ##STR1## wherein R.sup.1 represents a straight chain or branched chain alkyl or alkenyl group having 1-5 carbon atoms, R.sup.2 represents a straight chain or branched chain alkylene group having 1-8 carbon atoms or a phenylene group that may be substituted with a straight chain or branched chain alkyl group having 1-5 carbon atoms, A represent identical or different alkylene groups having from 2 to 4 carbon atoms, and n represents an integer from 0-100.