Complex dielectric permittivities for parallel orientations of the director n, with the probing electric field E (Eparallel ton()), of the weakly polar liquid crystal (LC) 4,4'-di-n-hexylazoxybenzene (D6AOB) dispersed with hydrophobic and hydrophilic aerosils, have been measured in the frequency range 20 Hz to 30 MHz. In the nematic phase of D6AOB dispersed with hydrophobic and hydrophilic aerosils, significant changes in the dielectric properties are observed. An additional slow process due to the restricted motion of the molecules in surface layers is observed for hydrophilic samples. The slow process is absent in the hydrophobic samples suggesting that in the LC-hydrophilic aerosils a surface layer is formed at the aerosil interface. The process does not depend on temperature and has a wide distribution of relaxation times. The bulk-like rotation around the short axis for D6AOB dispersed with hydrophilic aerosils has been modified significantly. It seems that this could be due to an overlap between the main bulk-like process and a hindered rotation of molecules around their long axes for molecules that are oriented perpendicular to the probing electric field.