Cycloheptanol, cyclo-octanol, cyanoadamantane and cis-1,2-dimethylcyclohexane are known to form plastic crystals which can be supercooled to show a glass transition at a temperature T-g. The molecular dynamics in different plastic phases is studied in their supercooled states using dielectric spectroscopy (frequency range: 10(6) Hz-10(-3) Hz) and differential scanning calorimetry (DSC) over a wide temperature range. The kinetic freezing of the various dielectric processes have been critically examined in relation to the T-g found in the DSC experiments. The plastic phase I of cyclo-octanol shows two T-g's: one at 148.5 K and the other at 164 K, the former of which is not found in well annealed phase I. The dielectric alpha -modes correspond to the latter. Cycloheptanol exhibits many T-g's for the different plastic phases. Unlike the cyclic alcohols, the dielectric spectra of cyanoadamantane and cis-1,2-dimethylcyclohexane is clearly found to follow the Havriliak-Negami equation, both of which interestingly show very little molecular mobility, often referred to as the secondary relaxation in their glassy states. In addition, the temperature dependence of the relaxation rates and the dielectric strengths are critically examined for various supercooled phases to gain an insight into the nature of the molecular mobility in those phases. (C) 2001 American Institute of Physics.