The contribution is dedicated to the molecular dynamics (MD) simulations of the superionic ternary compounds of compositions AgxCu1-xI, x=0.0, 0.25, 0.5, 0.75, and 1.0. With the aid of the pair inter-atomic potentials of the form proposed by Vashishta and Rahman [Phys. Rev. Lett. 40 (1978) 139] for metal iodides, we performed the series of simulations in isothermal-isobaric (NpT) ensemble. The diffusion coefficients of the cations have been calculated from the mean square displacement (MSD) versus time relationship. The activation energies have also been estimated. The influence of stoichiometry and temperature on the diffusion process is discussed.