Stepwise annealing near the crystal-liquid crystal transition temperature was applied to a 73/27 4-hydroxybenzoic acid (HBA)/2-hydroxy-6-naphthoic acid (HNA) copolyester to increase the melting transition from 281 to 316 degrees C. An unexpected degradation process was observed when further annealing was applied at 305 degrees C. An irreversible loss of crystallinity was confirmed by differential scanning calorimetry (DSC) and wide-angle X-ray diffraction (WAXD). The melt rheology of the step ordered 73/27 HBA/HNA copolyester was investigated using a dynamic rheometer. In contrast to the untreated and ordered sample, the degraded material exhibited an increase in melt viscosity (0.3 orders) after heating at 370 degrees C for 1 min,indicating some form of irreversible reaction. Furthermore, a plot of storage modulus versus loss modulus showed a completely different pattern for the degraded material. These observations suggest that a small amount of branching or cross-linking has occurred in the 73/27 HBA/HNA copolyester during step annealing at 305 degrees C. An attempt was made to simulate this process by adding 1 wt % of a cross-linkable oligomer to the 73/27 HBA/HNA copolyester. From the melt viscosity, it could be concluded that a small. amount of branching (below 0.5 wt %) has occurred most likely in the crystalline regions of the ordered copolyester.