Recently, a hyperelastic-viscoplastic constitutive model was developed for PET and the noncrystallizing copolymer PETG (R. B. Dupaix, Ph.D. thesis, MIT, 2003). The materials were found to behave very similarly under monotonic loading conditions and the single constitutive model was able to capture both materials’ behavior. However, differences were observed upon unloading, and it is expected that additional differences would be observed under more complex loading conditions. Here their behavior is investigated under nonmonotonic loading conditions, specifically under load-hold conditions. The model of Dupaix and Boyce (R. B. Dupaix, Ph.D. thesis, MIT, 2003) is modified to include Ahzi’s upper-bound model for strain-induced crystallization [Ahzi, Mech. Mater., 35(12), pp. 1139–1148 (2003)]. The crystallization model is adapted to include criteria for the onset of strain-induced crystallization which depend on strain rate and level of deformation. The strain-rate condition prevents crystallization from beginning prior to the deformation process slowing significantly. The level-of-deformation condition delays crystallization until the material has deformed beyond a critical level. The combined model demonstrates differences in behavior between PET and PETG during complex loading situations, indicating its ability to capture the fundamental criteria for the onset of strain-induced crystallization.