A multi-component hair dye composition excellent in bleaching property and dyeing property including components (a), (b) and (c) which are mixed upon use:(a) one or more kinds of glycylglycine derivative represented by general formula (1) and having two or three amino acid residues, or salts thereof; [wherein X represents a bivalent hydrocarbon group having 1 to 4 carbon atoms which may be substituted with a hydroxyl group, or an amino acid residue; Y represents an amino acid residue, or a bivalent group represented by general formula (2): (wherein symbol -* represents a bond that binds to an adjacent carbonyl group or oxygen atom); R represents a hydrogen atom, or a monovalent hydrocarbon group having 1 to 4 carbon atoms in which the hydroxy group may be substituted; and m and n each represent 0 or 1, provided that when both m and n represent 1, X is not an amino acid residue]; (b) an alkali agent; and c) an oxidizing agent; wherein formula (I) is: