  We investigate the power-law tails in the evolution of a charged massless
scalar field around a fixed background of a dilaton black hole. Using both
analytical and numerical methods we find the inverse power-law relaxation of
charged fields at future timelike infinity, future null infinity, and along the
outer horizon of the considered black hole. We invisage that a charged hair
decays slower than neutral ones. The oscillatory inverse power law along the
outer horizon of the dilaton black hole is of a great importance for a mass
inflation scenario along the Cauchy horizon of a dynamically formed dilaton
black hole.
