In the present communication, dielectric relaxation investigations on three interesting supercooled plastic crystalline substances, i.e., isocyanocyclohexane (ICNCH), cyanocyclohexane (CNCH), and 1-cyanoadamantane (CNADM) are reported. All of these have the main dipole moment situated in their side group- C[Triple Bond]N or- N[Triple Bond]C. Differential scanning calorimetry (DSC) was also employed as a supporting technique. Glassy crystal were easily formed in the first two samples by slowly cooling the plastic phase, but in CNADM it was formed by rapidly quenching the room temperature plastic phase. In addition to the so called alpha process that can reasonably be described by a Havriliak-Negami (HN) shape function, a secondary (or beta) relaxation process is found in all the materials. The beta process in CNADM has an activation energy (DeltaE(beta)) of about approximately 13.8+/-1 kJmol, and is present even in the corresponding ordered crystalline phase, i.e., in its monoclinic phase. On the other hand, the magnitude of DeltaE(beta) in both the isomers of cyanocyclohexane, i.e., ICNCH and CNCH, is similar and is about 21.1 and 23.4 kJmol, respectively. Unlike CNADM, the cyclohexane derivatives are capable of exhibiting additional intramolecular process due to chair-chair conversion (i.e., in addition to the rotational motion of the side group- C[Triple Bond]N or- N[Triple Bond]C). Therefore, the secondary process of these systems is compared to that occuring in the binary liquid glass formed by dispersing a small quantity of these dipolar liquids in nearly nonpolar orthoterphenyl (OTP). Measurements were also made in the supercooled binary mixures of other cyclohexyl derivatives like cyclohexylchloride and cyclohexylbromide with OTP which lack a flexible side group. The sub-T(g) relaxation process exhibited in all these cases have almost similar activation energy as in case of pure ICNCH and CNCH. These observations together with the fact that the activation energy for this process is much below that of chair-chair conversion which is about 43 kJmol leads us to the conclusion that sub-T(g) relaxation process in the binary mixtures is JG type, and perhaps beta relaxation process in phase I of ICNCH and CNCH is also similar. With the help of semiemperical calculations of the dipolemoments for the axial and equitorial confirmers, it is concluded that the process associated with the chair-chair may not be dielectrically very active and, hence, should be relatively weaker in magnitude. The beta process in CNADM has an activation energy (DeltaE(beta)) of about 13.8+/-1 kJmol, and is present even in the corresponding ordered crystalline phase indicating that it may not be characteristic of the glass formation of phase I. The molecular structure of CNADM is such that it does not possess other intramolecular degrees of freedom of the type equitorial to axial (or chair-chair) transformation. Our experimental finding that JG relaxation for CNADM dispersed in glassy OTP matrix is about 31 kJmol, indicating that the well ...