Na-mordenite zeolite was cation-exchanged to obtain Li-, Li/Ag- and Ag-mordenite and treated with NH4F to obtain Na-, Li-, Li/Ag-mordeniteF (M) and Na-mordeniteF (10%). Samples were characterized by XRD, nitrogen physisorption, Al-27 and Si-29 MAS NMR, FTIR spectroscopy, and X-ray fluorescence. Special attention was given to the presence of F- ions in the mordenite structure. Equilibrium adsorption isotherms of high-purity components N-2 and O-2 were measured at 298 K. For the cation-exchanged mordenite samples, the adsorbed nitrogen volume is slightly higher than that obtained in other zeolites such as zeolite X with a lower Si/Al ratio. This reveals the significant influence of the cation's accessibility to the gas molecules in these adsorption processes. N-2 adsorption capacity increases in the order Na+ < Ag+ < Li+, whereas the N-2/O-2 adsorption selectivity varies as Na+ < Li+ < Ag+ for the cation-exchanged mordenite samples. In samples prepared by fluorinated treatment, the effect is different depending on the extraframework cation present. When Na+ and Li+ cations are present, F atoms decrease the shielding caused by the walls to the cation's charge resulting in an increase on the adsorption selectivity, especially at low pressures, with a slight decrease in the number of active sites. However, the effect of F on Ag+ cations is mainly an electronegative effect, making the adsorbate-adsorbent interaction less favorable.