Rigid-rod polymers produced in the past are, in general, highly insoluble (except in the special case of polymers with basic groups which may be dissolved in strong acid) and are infusible. These properties make them difficult, and often impossible, to prepare and process. We have found, surprisingly, that the incorporation of appropriate pendant organic side groups to the polymer substantially improves solubility and fusibility. Earlier work has suggested that such pendant side groups do not increase the solubility of rigid-rod polymers. However, by increasing the size of the side chain and/or by matching its properties (principally, polarity and dielectric constant) to the polymerization solvent, rigid-rod polymers of substantial molecular weight can be prepared. For example, when the polymerization is carried out in a polar solvent, such as dimethylformamide, the solubilizing organic side groups will preferably be polar and will have high dielectric constants, such as dielectric constants greater than 5.