Polymer/clay nanocomposite materials based on poly(propylene-graft-maleic anhydride) (PPgMAH) and two different organophilic modified clays were investigated by dielectric relaxation spectroscopy (DRS). In contrast to ungrafted polypropylene (PP), PPgMAH shows a dielectrically active relaxation process which can be assigned to localized fluctuations of the polar maleic anhydride groups. Its relaxation rate exhibits an unusual temperature dependence, which could be attributed to a redistribution of water molecules in the polymeric matrix. This is confirmed by a combination of Raman spectroscopy and thermogravimetric experiments (TGA) with real-time dielectric measurements under controlled atmospheres. In the nanocomposites this relaxation process is shifted to higher frequencies up to 3 orders of magnitude compared to the unfilled polymer. This indicates a significantly enhanced molecular mobility in the interfacial regions. In the nanocomposite materials a separate high-temperature process due to Maxwell-Wagner-Sillars (MWS) polarization was observed. The time constant of this MWS process can be correlated with characteristic length scales in nanocomposites and therefore provides additional information on dispersion and delamination/exfoliation of clay platelets in these materials. These properties also influence the diffusivity of the water molecules as revealed by real-time dielectric investigations.