The relationship was determined between sub‐Tg molecular motions and the transport of O2 and CO2 in amorphous polyesters and copolyesters based on poly(ethylene terephthalate) [PET] and poly(1,4‐cyclohexylenedimethylene terephthalate) [PCDT], Modifications of the polyester with certain acid co‐monomers restricted the molecular motions that occurred in the β‐relaxation region and in turn decreased the O2 diffusion coefficient. The solubility coefficient was unchanged by those modifications. Modification of PET with 1,4‐cyclohex‐anedimethanol increased the magnitude of the β‐relaxation and both the diffusion and solubility coefficients of O2. Similar relationships between the β‐relaxation magnitude and CO2 permeability were also found. The temperature dependence of O2 permeability followed an Arrhenius relationship, with different activation energies (Ep) above and below the β‐relaxation. The activation energy was smaller below the β‐relaxation. Values of Ep above and below the β‐relaxation did not depend on the chemical structure of the polymer.