The lattice theory of hard rods with anisotropic dispersion forces presented recently is extended to the case where the rods are dispersed in a diluent. Two systems are treated: (i) rods of axial ratio χ diluted with solvent molecules having χ = 1, and (ii) rods of axial ratio χα mixed with homologs of axial ratio χ β. Treatment of the latter system can be regarded as an extension of the Flory and Abe theory for "athermal" polydisperse systems, in which dispersion forces are inconsequential. Solutions of sufficiently long (χ > 20) rods subject to anisotropic dispersion forces are predicted to exhibit complex phase equilibria involving a re-entrant nematic phase (with a critical point) and a triple point, as well as the usual nematic-isotropic coexistence. These deductions should be relevant to thermotropic solutions of rodlike synthetic polymers with phenylene groups or other groups exhibiting anisotropic interactions. Calculations for mixtures of short rods yield more prosaic phase diagrams. It is suggested that such systems (for example, mixtures of the polyphenyls) can provide comprehensive tests of the underlying theory. Mixtures of quinque- and quaterphenyl are specifically considered. © 1980 American Institute of Physics.