Nanocomposites based on polypropylene (PP) and organically modified ZnAl layered double hydroxides (ZnAl-LDH) were prepared by melt blending and investigated by a combination of differential scanning calorimetry (DSC), small- and wide-angle X-ray scattering (SAXS and WAXS), and dielectric relaxation spectroscopy (DRS). An average number of stack size of LDH layers is calculated by analyzing the SAXS data which is close to that of pure organically modified ZnAl-LDH. Scanning microfocus SAXS investigations show that the ZnAl-LDH is homogeneously distributed in the PP matrix as stacks of 4-5 layers with an intercalated morphology. DSC and WAXS results show that the degree of crystallinity decreases linearly with the increasing content of LDH. The extrapolation of this dependence to zero estimates a limiting concentration of ca. 40% LDH where the crystallization of PP is completely suppressed by the nanofiller. The dielectric spectra of the nanocomposites show several relaxation processes which are discussed in detail. The intensity of the dynamic glass transition (beta relaxation) increases with the concentration of LDH. This is attributed to the increasing concentration of the exchanged anion dodecylbenzenesulfonate (SDBS) which is adsorbed at the LDH layers. Therefore, a detailed analysis of the beta-relaxation provides information about the structure and the molecular dynamics in the interfacial region between the LDH layers and the polypropylene matrix which is otherwise dielectrically invisible (low dipole moment). As a main result, it is found that the glass transition temperature in this interfacial region is by 30 K lower than that of pure polypropylene. This is accompanied by a drastic change of the fragility parameter deduced from the relaxation map.