The simulation of 4 K H-1 broad-line NMR spectra of CD3OH interacting with the acidic OH groups of H-mordenite zeolite shows no CD3OH2+ ions but hydrogen-bonded complexes. For high CD3OH concentrations, clusters of hydrogen-bonded methanol molecules are formed, also hydrogen-bonded to Bronsted acid sites of the zeolite. The 300 K H-1 MAS spectra prove that the desorbed H-mordenite sample contains also silanol groups in electrostatic interaction with the framework; these silanols do not interact with methanol under our experimental conditions.