For most of amorphous polymers the long term viscoelastic behaviour is greatly affected by physical aging, referring to their non-equilibrium structure approaching the equilibrium state, which influences thermomechanical properties. This study successfully applies a constitutive model, originally developed for semi-crystalline polyesters to characterise the effect of physical aging on stress relaxation and creep of two glycol modified poly(ethylene terephthalate) grades, (poly(ethylene-co-1,4-cyclohexylenedimethylene terephthalate) (PECT) and poly(ethylene-co-2,2,4,4-tetramethyl-1,3-cyclobutanediol terephthalate) (PETT). Both copolyesters are subject to annealing at Tg-20 °C for up to 504 h and subsequent uniaxial stress relaxation tests and, for PECT, creep tests. The results show that annealing time has a significant influence on the viscoelastic behaviour increasing the resistance to creep and stress relaxation. The effect of physical aging on model parameters is described and analysed while it is found that the concentration of active polymer junctions decreases exponentially with annealing time. Generally, PETT and PECT showed almost identical viscoelastic behaviours at 30 °C, suggesting that the chemical structure of the glycol unit (2,2,4,4-tetramethyl-1,3-cyclobutanediol and 1,4-cyclohexylenedimethanol) does not have significant effect on their viscoelasticity. When stress relaxation is tested at elevated temperatures, the structural effects are more visible, demonstrating higher activation energies for PETC than those for PETT. Physical aging is also found to decrease activation energies from 326.6 to 128.1 kJ mol-1 for PECT and from 262.7 to 78.5 kJ mol-1 for PETT, demonstrating a weaker effect of temperature in aged samples.