The magnetic excitations of Fe_1-pMg_pCl₂ have been studied using a numerical method involving the time integration of the equations of motion. Calculations were performed on a 10000 site, randomly disordered two-dimensional model alloy. The spectral response function was calculated for the whole range of dilution p at various points in the Brillouin zone. The results obtained are compared with experimental data and with other theoretical calculations, in particular the moment expansion method of Fujiwara (1977).