Foam quality and discharge properties are improved by using a squeeze container to discharge a mixed solution of first and second agents of a two-part hair cosmetic for hair dyeing or bleaching in a foam. A two-part hair cosmetic 1 for hair dyeing or bleaching includes a first agent A1 containing an alkaline agent and a second agent A2 containing hydrogen peroxide and a squeeze container 6 for discharging a mixed solution A3 of the first agent A1 and the second agent A2. The first agent A1 or second agent A2 contains a foaming agent. The mixed solution A3 thereof has a viscosity (25°C) of from 1 mPa·s to 100 mPa·s. A squeeze foamer 5 of the squeeze container 6 has a gas-liquid mixing chamber 12 for causing the mixed solution to foam, foam homogenizing means 14 for homogenizing foam of the mixed solution which has been made to foam in the gas-liquid mixing chamber 12, and a discharge outlet 17 for discharging the homogenized foam. The ratio between the total volume of the first and second agents and the inner volume of the container body is in the range of from 0.30 to 0.60. The torso cross-section of the container body has a ratio of minor axis to major axis of from 0.5 to 1.0, and an area of from 12 cm2 to 30 cm2.
