High-T-g yet mechanically robust polymers are desirable but difficult to realize. To explore whether the insertion of a motionally active molecular entity in the backbone could produce polymers with both high T-g and yet are not brittle, three series of high-T-g glassy polycarbonates/polyesters/poly-(ester carbonate)s were designed and synthesized. The secondary relaxation behavior of these polymers was studied by dynamical mechanical analysis (DMA). Incorporation of cyclohexylene groups (C-rings) in the main chain of polymers made from two rigid and bulky monomers, spirobiindane bisphenol (SBI) and trimethylcyclohexylbisphenol (Tmc), respectively, changes the gamma relaxation process dramatically in peak shape and position in these polymers. No such change is observed in polycarbonate polymers made from cyclohexylbisphenol (BPAZ), or ZPC for short. Through monitoring the gamma relaxation with gradual structural change, C-rings in the main chain backbone are proposed to undergo active ring inversion. The gamma relaxation of ZPC is proposed to be mainly due to side-chain C-ring inversion. The narrowing on the high-temperature side of the gamma relaxation peak of the polycarbonate of Tmc is proposed to be due to the restricted motion of its axial phenyl rings. A linear correlation between relaxation strength and total C-ring concentration was found for all the polymers.