The third-order nonlinear optical susceptibility ͑3͒ ͑Ϫ3;,,͒ of thin films of poly͑p-phenylenevinylene͒ ͑PPV͒ and several corresponding oligomers ͑OPV-n͒ has been investigated by third-harmonic generation using variable laser wavelengths from 900 to 1520 nm. The oligomers show a single three-photon resonance of ͑3͒ ͑Ϫ3;,,͒ which is closely related to the linear absorption spectrum. We can identify, however, two maxima in the ͑3͒ spectrum of PPV. They are assigned to three-photon resonances with the maximum of the exciton absorption and with the threshold of the continuum of states, which can be located at 3.2Ϯ0.1 eV. This corresponds to an exciton binding energy of 0.7Ϯ0.1 eV. We observe a general scaling behavior for PPV, OPV-n, and other one-dimensional conjugated -electron systems in their neutral form. Their ͑3͒ values, evaluated at comparable resonant or low-resonant conditions, follow an empirical scaling relationship(3) /␣ max ϳ max x , where ␣ max and max denote the absorption coefficient and wavelength of the low-energy absorption maximum. We obtain an exponent xϭ10Ϯ1 which is much larger than expected from an earlier theory. Possible reasons for the difference between theory and experimental results are discussed.