Nutation consists in monitoring the motion of nuclear magnetization under the application of a radiofrequency (rf) field. With an appropriate amplitude of the rf field, the nutation frequency depends on the NMR relaxation times. This property offers the possibility of differentiating species having the same Larmor frequency but differing by their relaxation times. This may occur for the composite proton NMR signal of water in complex systems. Separate nutation signals are thus observed with the possibility of measuring their longitudinal relaxation times by simply applying a saturation hard pulse, followed by an evolution interval, prior to the nutation sequence. This novel experiment has been used for studying the two sites existing for water in two kaolinite samples (one hydrated after stabilization of several months and the other nonhydrated). It turns out that water in these two sites differs essentially by its transverse relaxation time. Moreover, recovery is surprisingly biexponential for these two signals. A proper analysis of results obtained by this saturationrecovery nutation experiment provides not only the specific longitudinal relaxation rates of water in these two sites but also information about the averaging which occurs at long evolution times. This is discussed with regard of the structure and organization of the clay network. In particular, from relaxation rates at short evolution times, it is shown that this network is mainly constituted of ordered platelets, with a relatively weak proportion of randomly distributed platelets.