The Miesowicz viscosities eta(c) and eta(b) of dilute nematic solutions of the main-chain liquid crystal polymer (LCP) TPBx, in 4'-(pentyloxy)-4-cyanobiphenyl (50CB) or 4'-pentyl-4-cyanobiphenyl (5CB) as nematic solvents, were measured by cone-and-plate rheometry in the presence and absence, respectively, of an external electric field. TPBx has a mesogenic group, 1-(4-hydroxy-4'-biphenyl)-2-(4-hydroxyphenyl)- butane, separated by flexible n-alkyl spacers of variable length x. Since for these solutions eta(c) >> eta(b), a pronounced electrorheological effect is observed, the viscosity with the field on being an order of magnitude larger than that with the field off. The intrinsic viscosity, [eta(c)], of TPB10 in 50CB, was found to follow a Mark-Houwink-Sakurada relationship, [eta(c)] = KM(alpha), with alpha approximate to 1.0. Applying a theoretical description by Brochard, this result suggests that TPB10 behaves hydrodynamically in 50CB like a free-draining random coil stretched along the director. Comparisons were made of [eta(c)] and [eta(b)] for TPBx and a hyperbranched LCP, TPD-b-8, based on a similar mesogen. From the ratio [eta(c)]/[eta(b)], via the Brochard model, the ratio (R(parallel to)/R(perpendicular to)) of the end-to-end distances of the LCP measured parallel and perpendicular to the nematic director were found to be similar to 2-2.5 for TPBx and similar to 1.45 for TPD-b-8, consistent with the expectation that the chain anisotropy of the branched species in the nematic state is smaller.