The secondary relaxations of a series of glassy copolymers based on poly(ethylene terephthalate) (PET) and poly( 1,4-cyclohexylenedimethylene terephthalate) (PCT) involve cooperative motions of the cyclohexylene rings. The cooperativity gives rise to longer range motions which create significant volume fluctuations that can facilitate macroscopic shear yielding. Comparison of the secondary loss peaks and activation energies by dynamic mechanical spectroscopy between the copolyesters and poly(cyclohexyl methacrylate) and poly(1,4-cyclohexylenedimethylene 2,5-dimethylterephthalate) indicates that the secondary relaxation of the copolyesters involve motions of the cyclohexylene ring. Dipolar rotational spin-echo C-13 NMR confirmed large amplitude motions of the cyclohexylene ring faster than 10 kHz at 300 K. By examining feasible ring conformations, we conclude that transitions between chair and twist-boat conformations are possible for trans-cyclohexylene rings and cis-rings that prefer chair conformations. (Cis-rings that reside in boat conformations are more restricted.)