Provided is a hair bleach or dye composition containing an amino-modified silicone, a highly polymerized silicone having a number-average degree of polymerization of 1000 or greater, a cationic polymer and an oxidizing agent. The hair bleach or dye composition of the present invention does not give a discomfort upon washing or shampooing of the treated hair, can bleach or dye the hair uniformly from root to tip without damaging the hair by this treatment, add to the hair a good color and luster, and a good feel of the hair, manageability and hair retention after drying, and is also good in durability of these effects and stability.
