Rheological properties of two copolyesters which exhibit liquid crystalline behavior in the melt state were determined using an Instron capillary rheometer. The two polymer melts with nematic liquid crystalline order consisted of copolymers of polyethylene terephthalate (PET) and 60 and 80 mole % of p_hydroxybenzoic acid (PHB). Data was also obtained on PET which was used as a control. Measurements included the temperature and shear rate dependence of viscosity, entrance pressure losses (_Pent), and die swell (Dj/D). The viscosity of the liquid crystalline melts are as much as two orders of magnitude less than those of PET at temperatures at which they are ordinarily processed. The extrudate actually contracts at the lower end of processing temperatures but does increase to values greater than one with increasing temperature for the liquid crystalline polymers. Although the die swell data indicate that there is negligible elastic recovery at the capillary exit, values of the ratio of _Pent to wall shear stress (_w) are considerably higher for liquid crystalline melts than for PET. Some explanation of these data is presented but more rheological measurements are needed before our understanding of these unique systems is complete.