Some hexa-substituted benzenes are known to exhibit molecular rotation in their crystalline phase, but this phenomenon is not very well understood. In this context, we have critically examined two materials, namely pentachloronitrobenzene and 2,3,4,5,6-pentabromotoluene over a wide range of temperatures, using dielectric spectroscopy and differential scanning calorimetry (DSC) to ascertain the nature of the above said relaxation. A relaxation process is found in the crystalline phase, which is slightly non-Arrhenius in its temperature dependence in the former and deviation from Debye behavior has been found in both the samples. This behavior is similar to that of the primary (or alpha-) relaxation found in glass forming materials. This phenomenon is found to correspond to a steplike (small) change in the specific heat in the DSC measurements indicating that it is a glass transition phenomenon. The sub-T-g relaxation data do not indicate any secondary (or beta-) process (of measurable magnitude). However, the same materials when studied in small quantities in the liquid matrix of o-terphenyl (nonpolar) indicated a considerable magnitude for the beta-process of molecules even below the liquid T-g of these mixtures. The results are discussed in the context of the glass transition phenomena of the above materials. (C) 2003 American Institute of Physics.