The interaction of N-2 and O-2 with extraframework cations of zeolite frameworks was studied by DFT, using the B3LYP method. The extraframework cation sites located in the vicinity of the double six-member rings (D6R) of FAU zeolites (SI, SI', SIII') were considered and clusters with composition (Mnn+)(2/n)H12Si10Al2O18, M = Li+, Na+, K+, Ca2+, were selected to represent the adsorption centers. The cation sites SII in the center of single six-membered rings (S6R) were modeled by [(MH12Si4Al2O6)-H-I](-) and (MH12Si4Al2O6)-H-II clusters. The adsorption energy of N-2 and O-2 is the highest for Li+ cations at the SIII' cation sites, while for the SI' and SII sites the adsorption energies decrease in the order Ca2+ > Na+ > Li+. The calculated small N-2 adsorption energy for Li+ cations at SII sites suggests that these sites do not take part in the sorption process in agreement with results of NMR studies and Monte Carlo simulations. The N-2 adsorption complexes with the extraframework cations are linear, while those of O-2 are bent regardless of the extraframework cation location. The SIII' cation sites are the most favorable ones with respect to N2 adsorption capacity and N-2/O-2 selectivity; the SII sites are less selective and the SI sites are not accessible.