Gas hydrate formation is considered one of the major problems facing the oil and gas industry as it poses a significant threat to the production, transportation and processing of natural gas. These solid structures can nucleate and agglomerate gradually so that a large cluster of hydrate is formed, which can clog flow lines, chokes, valves, and other production facilities. Thus, an accurate predictive model is necessary for designing natural gas production systems at safe operating conditions and mitigating the issues induced by the formation of hydrates. In this context, a thermodynamic model for gas hydrate equilibrium conditions and cage occupancies of N2 + CH4 and N2 + CO4 gas mixtures at different compositions is proposed. The van der Waals-Platteeuw thermodynamic theory coupled with the Peng-Robinson equation of state and Langmuir adsorption model are employed in the proposed model. The experimental measurements generated using a cryogenic sapphire cell for the pressure and temperature ranges of (5-25) MPa and (275.5-292.95) K, respectively, were used to evaluate the accuracy of this model. The resulting data show that increasing nitrogen mole percentage in the gas mixtures results in decreasing of equilibrium hydrate temperatures. The deviations between the experimental and predictions are discussed. Furthermore, the cage occupancies for the gas mixtures in hydrate have been evaluated. The results demonstrate an increase in the cage occupancy for both the small and large cavities with pressure.