The third-order nonlinear optical (NLO) properties of a series of poly(2,5-dialkoxy-p-phenyleneethynylene)s (PPEs) have been investigated in solution and in the solid state. In these PPEs, different alkoxy side chains are attached to the rigid-rod polymer main chain, leading to a series of polymers having an identical conjugated backbone but different supramolecular structures in the solid state. The nonresonant third-order NLO susceptibilities chi((3))(-3 omega;omega,omega,omega) were measured by third-harmonic generation experiments. chi((3)) values of up to 7.5 x 10(-20) m(2)/V-2 in solution and 14 x 10(-20) m(2)/V-2 in the solid state were determined. In solution, the NLO susceptibilities were found to be proportional to the content of polymer backbone, which depends on the functionalization of the PPEs. The solid state NLO susceptibilities were found to be related to the degree of long-range order in the samples, increasing with increasing order. In samples which adopt only a small extent of long-range order, the rigid-rod conjugated polymer backbones behave if they were "dissolved" in a hydrocarbon solvent, and consequently the nonlinear optical susceptibilities are comparable to those determined for solutions of these polymers. In films in which the polymer chains were found to adopt lamellar type supramolecular structures, the coplanar orientation of the conjugated polymer backbones is assumed to lead to intermolecular electronic interactions which give rise to extended conjugation lengths and hence lead to an increase of the nonlinear optical response.