A process for inhibiting hair fibers from becoming frizzy, involving contacting the hair fibers with a composition containing: (a) at least one polyamine compound having at least two amino groups; (b) at least one anionic silicone; (c) optionally, at least one surfactant; and (d) optionally, at least one film-forming polymer, and wherein (a) is present in the composition in an amount sufficient to inhibit dyed hair fibers from losing their color, as well as inhibit hair fibers, in general, from appearing frizzy.