The rheological properties of a liquid crystalline copolymer have been studied as a function of time at constant temperature. The changes which occur with increasing time include (i) an increase in η*, (ii) an increase in the non‐Newtonian character of the flow, and (iii) an increase in the elasticity of the melt. The initial changes occur over a time scale of approximately 10 min; slower increases are found for times up to 120 min. A possible explanation for the effects observed is crystallization, i.e., the changes in rheological properties result from the presence of a continually increasing crystalline phase. Additional evidence which supports this hypothesis is presented. From a DSC study of the annealing of the polymer at high temperatures, the dependence of the crystal melting temperature on thermal history is demonstrated. The increase in melting temperature which is observed is consistent with the explanation proposed for the rheological changes. Finally, the results of a study of the time dependence of the rheological properties of a model isotropic copolyester, Kodar PETG, are presented. In many respects, the structural and crystallization characteristics of PETG are similar to those of the liquid crystalline polymer studied. Similar time dependence was found for the rheological properties of PETG.