Viscoelastic properties for a series of all-aromatic main-chain thermotropic copolymers based on random units of 75% 1-hydroxy-4-benzoic acid and 25% 2-hydroxy-6-naphthoic acid (B-N, 3:1) were measured in the nematic state. Zero-shear rate viscosity eta(0) obtained from small-strain oscillatory and steady-state measurements reveals that eta(0) scales with the molecular weight with a power of 4.1, i.e., eta(0) proportional to M(4.1). Measurements of viscosity for the small-molecule liquid crystal (SMLC) bis[4-(phenoxycarbonyl)-phenyl] 1,4-benzenedicarboxylic acid ester and data for other SMLC compounds taken from the literature establish that this power dependence holds over a range covering 3 decades in molecular weight and 8 decades in viscosity. This exponent 4.1 is distinctly different from that of conventional polymer melts, 3.4, but lies within the range of values reported for nematic polymers with flexible spacers.