Both linear William-Watts (WW) and non-linear Narayanaswamy-William-Watts (NWW) stretch relaxation satisfactorily described the time dependent rigid amorphous phase growth kinetic. The model is tested upon the completely amorphous cyclic olefin copolymers (COC, polynorbornene/polyethylene copolymer), where a large Tg variation is detected with annealing. Increase of the rigid amorphous fraction as reflected in the increase of Tg, is attributed to the growth of short-range ordered phase due to the rigidity of the norbornene chain segment. The analysis shows the growth kinetic (represented by the retardation time, and the stretch exponent) that depends not only on the norbornene (NB) content but also on the NB microblock structure. The kinetics for the growth of the rigid amorphous domains follows a stretched exponential expression, similar to that given for polymer crystallization and physical aging.