This work is concerned with single ion dynamics in molten copper halides (CuI and CuCl) which exhibit fast ionic conduction before melting. The self-dynamic structure factor of the two ionic species in each melt have been calculated by molecular dynamics simulations and the corresponding effective wavelength-dependent self-diffusion coefficients have been studied. The results have been compared with those obtained for molten alkali halides (KCl and RbCl).