Provided is a two-part oxidative hair dye composition having a first agent containing an alkali agent and an oxidation dye intermediate or a direct dye and a second agent containing an oxidizing agent, wherein at least one of the first and second agents contains both of Components (A) and (B): (A) an iso-fatty acid or an anteiso-fatty acid having from 19 to 30 carbon atoms, or a salt thereof, and (B) a quaternary cationic surfactant.
