With the aim to investigate, by means of elastic neutron scattering, the effects produced by the cation substitution on the dynamics of water in zeolites, we measured, using a neutron backscattering spectrometer, the temperature dependence of mean-square atomic displacements [u2] derived from window integrated quasielastic spectra of fully and partially hydrated Na-A and Mg50-A zeolites. The results, collected in the 20-273 K temperature range, reveal that, at low temperature, the [u2] shows a harmonic trend independent of hydration and cation substitution, and, at higher temperatures, the onset of a non-Gaussian dynamics of the elastic intensity. This latter takes place at T approximately 200 K and approximately 150 K for fully and partially hydrated samples, respectively. This behavior has been interpreted in terms of reorientational jumps of H atoms described by two-site processes within an asymmetric double-minimum potential. In spite of its simplicity, the model seems to reproduce the rearrangement of the hydrogen bond network of zeolitic water. The fit results indicate a reduced proton mobility by diminishing the water content and by the induced Na+-->Mg2+ ion exchange, in agreement with previous incoherent quasielastic neutron scattering results at higher temperatures.