Temperature dependencies of Al-27 and Na-23 nuclear magnetic resonance spectra and spin-lattice relaxations in mordenite have been studied in static and magic angle spinning regimes. Our data show that the spin-lattice relaxations of the Na-23 and Al-27 nuclei are mainly governed by interaction of nuclear quadrupole moments with electric field gradients of the crystal, modulated by translational motion of water molecules in the mordenite channels. At temperatures below 200 K, the dipolar interaction of nuclear spins with paramagnetic impurities becomes an important relaxation mechanism of the Na-23 and Al-27 nuclei.