A statistical-thermodynamical lattice treatment of systems of chain molecules, previously developed to investigate the nematic/isotropic phase transitions of polymers with rigid and flexible parts alternating along the main chain, has been modified to study the mesophasic behavior of the title polymers. Two series of derivatives of poly(1,4-phenylene terephthalate) and of poly(1,4-oxybenzoyl), with alkyl groups of various lengths attached to the aromatic rings, have been modeled as proper sequences of isodiametric units placed at the nodes of the face-centered cubic lattice. In the hypothesis that the behavior of these polymers is mainly determined by the high rigidity of the main chains, rather than by anisotropic attractive interactions, and that the side chains can be treated as completely flexible, the model requires a single adjustable parameter, related to the inflexibility of the main chain. Using the same value of this parameter for all the members of each series, the existence of stable anisotropic phases is predicted for the investigated systems, in good semiquantitative agreement with experiments. Furthermore, the values assumed in the two cases by the inflexibility parameter are of the same order as those which can be deduced from the average molecular dimensions for the two classes of polymers. We have also performed calculations modeling solutions of the two base polymers (without side groups) in which the volume fraction of the solvent equals the volume fraction occupied by the side groups in the bulk substituted polymers of the two series. The results indicate that the lowering of the isotropization temperature caused by the presence of flexible side chains is nearly coincident with that calculated for the corresponding solutions (without the demixing in two phases characteristic of solutions of rigid rods).