Although progress has been made in the study of biodegradable polyesters, little attention was given to aliphatic/alicyclic copolyesters. For this reason, we have undertaken systematic studies on the aliphatic/alicyclic copolyesters. As a first step in our research, we have presented the material characteristics (e.g., thermal and mechanical properties) and the biodegradability in different biological environments for a series of the aliphatic/alicyclic copolyesters that were synthesized by polycondensation of succinic acid, 1,4-butanediol, and 1,4-cyclohexanedimethanol. The chemical composition of the aliphatic/alicyclic copolyesters plays an important role in controlling the material characteristics and biodegradability. For the copolyesters with a mole fraction of succinic acid-1,4-cyclohexanedimethanol <0.3, an adjustment of the optimum between physical properties and biodegradability seems to be feasible.