Water in mesoporous materials possessing a two-dimensional hexagonal structure has been studied by the variation of its NMR longitudinal relaxation time T-1 as a function of the static magnetic field value, or equivalently of the NMR measurement frequency. This technique, dubbed relaxometry, has been applied from 5 kHz (measurement frequency) up to 400 MHz with various instruments including a variable-field spectrometer operating between 8 and 90 MHz. Moreover, the range 0-5 kHz could be investigated by transverse relaxation, T-2 denoting the corresponding relaxation time, and relaxation in the rotating frame, T-1p denoting the corresponding relaxation time. Measurements of proton relaxation rates (inverse of relaxation times) have been performed with H2O and HOD (residual protons of heavy water) at water volumes of 80%, 60%, and 40% relative to the porous volume. Comparison between H2O and HOD shows clearly that, above 1 MHz where both sets of data are superposed, relaxation is purely intermolecular and due to paramagnetic relaxation (dipolar interactions of water protons with unpaired electrons of paramagnetic entities). Below 1 MHz, it is possible to subtract the intermolecular contribution (given by HOD data) from H2O data so that one is left with intramolecular relaxation which is solely due to water reorientational motions. The analysis of these low-frequency data (in terms of Lorentzian functions) reveals two types of water within the pores: one interacting strongly with the surface and the other corresponding to a second layer. High-frequency data, which arise from paramagnetic relaxation, exhibit again two types of water. Due to their correlation times, one type is assigned to relatively free water within the pores while the other type corresponds to bulk (interparticular) water. Their proportions, given as a function of the volume fraction, are consistent with the above assignments.