In this paper, several experimental techniques, i.e., differential scanning calorimetry, X-ray diffraction, Fourier transform infrared, Raman, and broadband dielectric spectroscopy were applied to study the nature of the phase transitions in 1-adamantylamine (1-NH2-ADM, C10H17N) and 1-adamantanol (1-OH-ADM, C10H16O). Calorimetric measurements showed one and three endothermic peaks in thermograms for the latter and the former substance, respectively. Indeed, results of spectroscopic investigations indicated that the observed thermal events in 1-NH2-ADM correspond to transitions between various plastic crystal (PC) phases (I, II, III, IV), while the endothermic process in 1-OH-ADM can be assigned to a phase transition between the PC and the ordinary crystal (OC). Especially interesting were the outcomes of dielectric studies carried out both at ambient and high-pressure conditions, during heating and cooling cycles. They showed: i) noticeable changes in the frequency dependencies of the imaginary (ε'') and real (ε') parts of the complex dielectric permittivity that occurred around temperatures of the characteristic endothermic events detected by the calorimetry, and ii) significant fluctuations of ε'' and ε' at pressures attributed to the respective phase transitions. Moreover, the pressure coefficients of the phase transition temperatures were estimated to be approximately equal to 0.2 K/MPa for both compounds. In turn, volume variation (ΔV) at the PC (II)-PC (III) and PC (III)-PC (IV) transition temperatures for 1-NH2-ADM was essentially different than ΔV for the PC-OC transition in 1-OH-ADM.