Thickness of silicide phases at Mo-on-Si and Si-on-Мо interfaces increases identically and linearly with a dose of irradiation at the small doses (by He$^{+}$ ions to $\Phi \leq 5\cdot10^{20}$ ion/m$^2$ and Ar$^{+}$ ions to $\Phi \leq 1.3\cdot10^{18}$ ion/m$^2$). Mean atomic composition of amorphous intermixed zones corresponds to alloys of MoSi$_{8.2}$ and MoSi$_{3.9}$ compositions under the irradiation by He$^{+}$ and Ar$^{+}$ ions, respectively. Density of the amorphous intermixed areas decreases when the irradiation dose increases. There are two areas corresponding to weak dependence ($T_{irr} \leq 260°C$) and strong dependence ($T_{irr} > 260°C$) of ion-beam mixing of Mo/Si multilayered structures irradiated by He$^{+}$ on irradiation temperature. Activation energies of the ion-beam mixing are equal $Q_{1} \approx 0.02$ eV и $Q_{2} \approx 0.5$ for the indicated areas, respectively. The features of the ion-beam mixing are explained by mixing in collision subcascades.