Synthetic Na-mordenite and Na-Y zeolites were studied by means of positron lifetime measurements and extended Doppler spectroscopy. From the lifetime and Doppler parameters (parapositronium peak, 3 gamma -annihilation ratio etc.) the influence of water on the formation and annihilation of orthopositronium (o-Ps) in the channels and cages was investigated. A comparison with thermogravimetry (TG) measurements has shown that the long-lived o-Ps component appears already at relatively high water content. The reversible temperature dependence at elevated temperatures might indicate thermal equilibrium of o-Ps with the zeolite lattice.