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 is presented to estimate hydrate formation conditions of binary and ternary gas mixtures. We performed molecular modeling of the 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 found that CO₂ was more favorable in occupying clathrate hydrate cavities than CH₄ or N₂. The addition of N₂ to the gas phase increased the ratio concentration of CO₂ in comparison with the concentration of CH₄ in clathrate hydrates and made gas replacement more effective. The mole fraction of CO₂ in the CO₂ + CH₄ + N₂ gas hydrate rapidly increased with the growth of its content in the gas phase, and the formation pressure of the CO₂ + CH₄ + N₂ gas hydrate rose in comparison to the formation pressure of the CO₂ + CH₄ gas hydrate. The obtained results agreed with the known experimental data for simple CH₄ and CO₂ gas hydrates and the mixed CO₂ + CH₄ gas hydrate.