A composition, kit and process for dyeing hair fibers in a manner which inhibits color loss during subsequent shampooing involving contacting the hair fibers with a composition containing: (a) at least one polyamine having at least two amino groups; (b) at least one anionic silicone; and (c) at least one dye component chosen from a direct dye and an oxidation dye, and wherein the dyed hair fibers inhibit color loss resulting from subsequent shampooing of the dyed hair fibers.