The effect of adding three different layered clays, a sodium montmorillonite and two commercial modified montmorillonites, on the morphology and molecular dynamics of natural rubber characterized by Transmission Electron Microscopy and Thermally Stimulated Depolarization Currents (TSDC) was studied. Carbon black was employed as reinforcing filler in a standard compound prepared and used for comparison purposes. The morphological results revealed that the sample with Cloisite\circledR 15A displays the highest degree of exfoliation, which suggests a stronger compatibility between the organic and inorganic phases. When the dispersion degree increases, a decrease of the activation energy was found from the quantitative analysis of the space charge dielectric relaxations.  From the qualitative analysis of the dipolar dielectric relaxations around $T_{g}$, changes in  the dielectric relaxation profile and in the peak localization were attributed to probable interactions between the nanofillers and the elastomer in the glass transition region of the NR.