A detailed study of the relaxation in the supercooled plastic crystalline phase has been carried out using dielectric spectroscopy and differential scanning calorimetry in cis-1,2 dimethylcyclohexane, neopentanol, cyclopentanol and a number of cyclohexyl derivatives to resolve the ambiguity regarding the glass transition temperatures, and the spectral shape. The various transitions (and the associated enthalpies) along with the glass transition temperature corresponding to the supercooled plastic phase are determined. The shape of the relaxation spectra and the temperature dependence of the relaxation rate are found to follow the strong and fragile pattern of Angell. Because of the difficulty in supercooling the liquid phase, the liquid-glass transition temperatures an determined in an indirect way using binary solution method. These transition temperatures are found to be about 6-9 degrees above that of the plastic crystal to 'glass' transition temperatures.