The sequential and random ring-opening polymerizations (ROP) of racemic-trans-cydohexene carbonate (rac-CHC) or enantiopure trans-(R,R)-cydohexene carbonate ((R,R)-CHC) with L-lactide (LLA) or trimethylene carbonate (TMC) have been performed. Catalytic systems based on zinc diaminophenolate [(NNO)ZnEt] ((NNO)(-) = 2,4-di-tert-butyl-6-{[(2'-dimethylaminoethyl) methylamino]methyl}phenolate)) or tris[N,N-bis(trimethysilyl)amide]yttrium (Y-[N(SiMe3)(2)](3)) complexes, or a guanidine-type organocatalyst (1,5,7-triazabicyclo[4.4.0]dec-5-ene, TBD), combined to an alcohol (BnOH or iPrOH) as initiator/chain-transfer agent were used. Well-defined diblock P(rac-CHC)-b-PLLA and P((R,R)-CHC)-b-PLLA and random P(rac-CHC)-co-PLLA and P(rac-CHC)-co-PTMC copolymers were thus synthesized with molar mass values up to M-n,M-NMR = ca. 34 000 g mol(-1) and rather narrow dispersity values (D-M = 1.2-1.7). H-1 and C-13{H-1} NMR characterizations of the copolymers revealed the presence of -OBn or -OiPr chain-end groups, thereby supporting the active role of exogenous alcohol as initiator. No decarboxylation reaction was ever observed during any copolymerization, thus providing PCHC/PLLA and PCHC/PTMC copolymers void of ether defects. Thermal analysis of the copolymers assessed by DSC and TGA confirmed their block or random structure. The block PCHC-b-PLA. and the random PCHC-co-PLLA and PCHC-co-PTMC copolymers represent the first examples of such copolymers synthesized by ring-opening copolymerization of the two comonomers. The latter PCHC-co-PTMC copolymers randomly combining CHC and TMC units are the first examples ever reported.