In this work, nitrogen and oxygen hydrate equilibrium conditions have been determined for the pressures up to 439 MPa using a modified van der Waals-Platteeuw (vdW-P) method by taking into account the double occupancy of large cages. A total of 148 literature hydrate data, inchiding 101 nitrogen hydrate data and 47 oxygen hydrate data were used to validate our calculations. Double occupancy was considered for the large cages of structure II. The gas-gas interactions were calculated using the Kihara potential model, in which the Kihara parameters were obtained using the pure nitrogen and oxygen second virial coefficients data. The Kihara parameters for the gas-water interactions were determined using pure nitrogen and pure oxygen hydrate equilibrium data. In contrast to previous models, the movement of two guest molecules were considered in the large cavities. The effect of pressure on molar volume differences between the empty hydrate lattice and liquid water was also considered. The solubilities of nitrogen and oxygen in water were calculated by flash calculation. For the case of comparison, the modified form of the van der Waals-Platteeuw (vdW-P) model presented by Parrish and Prausnitz was also applied. It is clarified that the double occupancy of large cages is a very important phenomenon at high pressures. The results showed that our modified model can decrease the errors of the vdW-P model by about 97%. The average absolute deviation of the presented model is about 0.13 K for nitrogen and oxygen hydrates. Additionally, the effect of the furthest water molecules in the three-layer model was also taken into account for calculation of the Langmuir constants. It is interpreted from the results that the effect of a three-layer model on gas hydrate calculations is not significant for oxygen and nitrogen hydrates. (C) 2016 Elsevier B.V. All rights reserved.