In this contribution, a method based on a solid solution theory of clathrate hydrate for multiple cage occupancy, host lattice relaxation and guest-guest interactions has been presented to estimate hydrate formation conditions of binary and ternary gas mixtures. We have performed molecular modeling of structure, guest distribution, and hydrate formation conditions for the CO₂ + CH₄, and CO₂ + CH₄ + N₂ gas hydrates. In all considered systems with and without N₂, at high and medium content of CO₂ in the gas phase we have found that CO₂ is more favorable to occupy clathrate hydrate cavities than CH₄ or N₂. Addition of N₂ to the gas phase increases ratio concentration CO₂ in compressing with concentration CH₄ in clathrate hydrates and makes gas replacement more effective. The mole fractions of CO₂ in CO₂ + CH₄ + N₂ gas hydrate rapidly increases with the growth of its content in the gas phase. And the formation pressure of CO₂ + CH₄ + N₂ gas hydrate rises in comparison with the formation pressure of CO₂ + CH₄ gas hydrate. Obtained results agree with the known experimental data for simple CH₄, CO₂ gas hydrates and mixed CO₂ + CH₄ gas hydrate.