Steady shear flow viscosities was measured for nematic liquid crystals (LCs) in the aromatic copolyesters composed of 4-hydroxybenzoic acid (HBA), 6-hydroxy-2-naphthoic acid (HNA), telephthalic acid, and biphenol whose molar contents are 0.73 - x, 0.27 - x, x, and x, respectively. Second harmonic generation (SHG) measurements showed that a SHG-active polar nematic LC formed by poly(HBA/HNA) with x = 0 is altered to a conventional nonpolar nematic LC with an increase in x more than 0.07. The shear-rate dependence of melt viscosity measured for nematic LCs of all the copolymers showed four characteristic regions; a Newtonian plateau in lowest shear-rate region 0 in addition to the well-known three regions, low-shear-rate shear-thinning region I, intermediate Newtonian plateau region II and high-shear-rate shear-thinning region III. The SHG-activity in nematic LCs reflected on the Newtonian plateau region 0. The viscosity of the SHG-active nematic LCs in this region 0 was 10 times higher than that of the non-SHG-active nematic ones. The higher viscosity of the SHG-active nematic LC was connected to the smaller domain size (or larger number of disclinations) estimated by small-angle light scattering. In the nonpolar nematic LC, many disclinations initially formed were easily annihilated because of a coalescence of two disclinations with opposite signs, whereas in the polar nematic LC, such an annihilation hardly Occurred because of the polar packing symmetry.