Nanocomposites with a predominantly exfoliated morphology were prepared by melt blending of organically modified doubled layered hydroxide (LDH) and low density polyethylene (PE). The prepared materials were investigated by differential scanning calorimetry (DSC) and in detail by dielectric spectroscopy. The DSC experiments show that the degree of crystallinity decreases linearly with increasing content of the LDH. The extrapolation of this dependence to zero results in a limiting concentration of ca. 50 wt % LDH were the crystallization of PE is completely suppressed by the nanofiller. The dielectric response of pure polyethylene shows different weak relaxation processes. The intensity of dynamic glass transition (beta-relaxation) increases with the concentration of LDH. This is attributed to the increasing concentration of the exchanged anion dodecyl benzene sulfonate (SDBS). The SDBS molecules are strongly adsorbed at the exfoliated 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 exfoliated LDH layers and the polyethylene matrix. This analysis shows that the beta-relaxation region consists of two processes: both of them obey glassy dynamics. The difference in corresponding Vogel (ideal glass transition) temperatures is about 30 K. The relaxation process at lower frequency is assigned to polyethylene segments with a reduced molecular mobility close to LDH layers. The process at higher frequencies is related to polyethylene segments in a farer distance for the surface of the nanofiller. In the nanocomposite materials an additional 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 the LDH layers in these materials.