Picosecond third harmonic generation (THG) spectroscopy in the range 0.9-2.4 mu m (0.52-1.38 eV) and sum-over-states (SOS) theoretical modeling have been used to investigate the third-order nonlinear optical properties of a series of nine conjugated aromatic polyimines designed to elucidate structure-chi((3)) relationships in conjugated polymers. The THG-measured frequency-dispersed third-order susceptibility (chi((3))) of the series of polymers has off-resonant and three-photon resonance-enhanced values in the ranges of 1.1 x 10(-12) to 2.0 x 10(-11) and 6.4 x 10(-12) to 7.2 x 10(-11) esu, respectively, demonstrating a large modulation of nonlinear optical response by simple structural variations. A random copolymer was found to have enhanced chi((3)) compared to either of its parent homopolymers. Asymmetric donor side-group substitutions were found to result in 7-10-fold enhancement of off-resonant chi((3)) compared to either symmetric substitutions or no substitutions. Theoretical three- and four-level SOS models, justified by site-selective fluorescence spectroscopy, were found to describe the chi((3)) dispersion data and the observed multiphoton resonances very well. The zero-frequency chi((3)) was predicted from the SOS models to be negative for eight of the nine polymers and to be in the range of -0.43 to -8.12 x 10(-12) esu, the magnitudes of which are very close to the observed off-resonance values at 2.4 mu m (0.52 eV). A negative real part of chi((3))(-omega;omega,-omega,omega) over a wide wavelength range of lambda > 1.38 mu m was also predicted by the SOS models for the same eight polymers with strong one-photon and two-photon resonances, suggesting that they would exhibit self-defocusing phenomena. Similarly predicted chi((3))(-omega;omega,-omega,omega) spectra of the poly(azomethines) suggest that third-order susceptibility measured by degenerate four-wave mixing would be up to 2 orders of magnitude larger than the values measured by THG spectroscopy.