The purpose of this paper is to depict the effect of diffusion and internal heat source on a two-temperature magneto-thermoelastic medium. The effect of magnetic field on two-temperature thermoelastic medium within the three-phase-lag model and Green-Naghdi theory without energy dissipation i discussed. The analytical method used to obtain the formula of the physical quantities is the normal mode analysis. Numerical results for the field quantities given in the physical domain are illustrated on the graphs. Comparisons are made with results of the two models with and without diffusion as well as the internal heat source and in the absence and presence of a magnetic field.