The interaction of CO with alkali metal-exchanged mordenite has been investigated by means of IR spectroscopy and calorimetry along with theoretical calculations based on DFT corrected to coupled-cluster accuracy (DFT/CC). It has been convincingly shown that Li+ is at least partially exchanged into the constricted part of the MOR structure as manifested by the low-frequency band at 2181 cm−1 and the isosteric heat of 44 kJ/mol. In the case of Na-MOR samples, significant changes have been observed in the stabilities of high- (2177 cm−1) and low-frequency (2165 cm−1) bands upon CO desorption, with the change of the Si/Al ratio from 40 to 9. Based on the kinetic measurements, it can be concluded that a crucial role in the MOR material is played by diffusion limitations, which are significantly influenced by the Si/Al ratio and the size of the cations. Similar effects also result in the increased stability of the 2138 cm−1 band of Na/K-MOR samples with higher Al content, where the “gate” effect is observed upon N2 adsorption. The dual cationic sites are directly observed only for the K-MOR sample via the weak band around 2150 cm−1. The formation of dual cationic sites cannot be completely ruled out in the case of Na-MOR, but their presence is most likely hidden in the low-frequency band.