The dynamic mechanical thermal properties of poly(hexamethylene terephthalate) (PHT), poly(1,4-cyclohexylenedimethylene terephthalate) (PCT) and their P(HT-co-CT) random copolymers in the amorphous state were examined as a function of temperature and frequency. All the samples exhibited two main relaxation processes in the plot of tan ${delta}$ versus temperature: the primary ${alpha}$-relaxation associated with the glass transition and the secondary ${eta}$-relaxation attributed to the local segmental motions of mostly cyclohexylene rings for PCT and to cooperative motions of methylene, carboxyl, and phenylene groups for PHT. Both ${alpha}$- and ${eta}$-relaxation temperatures increased with increasing CT content. The activation energy of the ${alpha}$-relaxation increased with increasing CT content, whereas that of the ${eta}$-relaxation decreased. The sub-glassy secondary ${eta}$-relaxation processes of PCT and PHT were investigated in terms of the cooperativity of main-chain segmental motions.