The main aim of the present investigation is to see how various relaxation processes including the chair–chair transformation (as found by earlier researchers at room temperature in mechanical relaxation spectroscopy) in cyclohexane derivatives evolve as the temperature is lowered. For this purpose, four remarkable (two-component) solid solutions that are orientationally disordered are investigated, where the first three systems are hydrogen (H-) bonded pairs, and the fourth is a non-H bonded pair. The former group is the two-component system of cyclohexanol (CHXOL) + 2,2-dimethyl-1-propanol or neopentanol (NPOL); cyclohexanol (CHXOL) + cycloheptanol (CHPOL) & neopentanol (NPOL) + neopentylglycol (NPGOL) systems, and the lone non H-bonded pair that has been studied is cyanocyclohexane (CNCH) and cyclohexylchloride (CHC). In all these cases, the liquid mixtures on cooling form orientationally disordered phases which are a solid solution of the corresponding pure phases. The feature is common to all the four systems studied here, but in CHXOL + CHPOL, the phase I of CHXOL beyond xm≥ 0.1 only forms a solid solution (designated as SI′) with the phase I of CHPOL. In CNCH + CHC the solid phase is stable for the concentration range 0 ≤xm≤ 0.4 (without transition to any other phase). The above solid phase I (or I′) has been investigated at low temperatures and for several concentrations, by means of dielectric spectroscopy and differential scanning calorimetry (DSC). Depending upon the concentration, this phase reveals a glass transition in the temperature range 116–150 K and associated with this is a pronounced relaxation process identifiable with the so called α-process. The dielectric spectra of this process is found to follow the Havriliak–Negami (HN) equation. In context of the binary system study here, the analysis of the various parameters obtained show an isomorphic relationship between the phases of the pure components through a continuous change of parameters. Another process of much smaller magnitude designated as the α′-process was also found in systems consisting of cyclohexyl derivatives above the glass transition temperature Tg which kinetically freezes around 170 K. This process interestingly, is also non-Arrhenius in nature, becomes increasingly weaker with increase in the second component, and may be identified with (axial) chair–(equatorial) chair transformation. In addition in all these systems, a weak high-frequency process and a clear sub-Tg process, are found which are designated as the β- & γ-processes respectively. The β-process may be identified with Johari–Goldstein (JG) or βJG process as it is found to follow the predictions of the coupling model proposed by Ngai. However, the identification of the γ-process with internal degrees of freedom are fraught with some problems in the interpretation of the experimental data that are highlighted. The kinetic freezing of the various dielectric processes have been critically examined in relation to the Tg found in the DSC experiments.