Complexes of methane molecules with cationic sites of alkali (Li, Na, K, Rb, Cs) and alkaline-earth metal (Mg, Ca, Sr, Ba) forms of zeolites have been studied theoretically using a density functional (DF) method. The modification of the cationic action due to the presence of a fragment of the zeolite framework Z = ALH(OH)(3)(-) has explicitly been taken into account by employing extended model clusters. Compared to the simpler models Mn+-CH4, these more adequate clusters ZM(n+)-CH4 yielded improved agreement between calculated and experimental IR spectroscopic data for methane in metal-exchanged high-silica zeolites M-Mor and M-ZSM-5. However, binding and vibrational parameters as computed in both types of models are similar and thus do not admit a rationalization of the unusual trend in the IR data found recently for methane adsorbed on cationic Na+ and Cs+ sites of zeolites with a low Si/Al ratio. A bifunctional mode of CH4 adsorption in the latter systems is discussed as a possible explanation for the observed IR characteristics.