Sum over states - complete neglect of differential overlap/spectroscopic parameterization plus configuration interaction, SOS - CNDO/S CI, is used to calculate the dispersion of the second order hyperpolarizability, gamma(-3 omega; omega, omega, omega) and gamma(-2 omega; 0, omega, omega), of five fullerenes, namely C-60, C-70, C-76, C-84(D-2), and C-84(D-2d). Very recent gamma(-omega; omega, omega, -omega) dispersion data for C-60 are also simulated. The five all-carbon molecules studied are available in sufficient quantities to allow for direct experimental measurements. All the Orr Ward diagrams are included in the calculation. Both the real and the imaginary part of the response are calculated. The results show good agreement with the experimentally available data for C-60 and C-70. The calculated static second order hyperpolarizabilities of the five molecules studied scale with the fourth power of the mass of the cluster. At energies lower than the one-photon absorption, the calculated gamma(-3 omega; omega, omega, omega) dispersion of the five fullerenes shows at least major resonances. The analysis of the differences between computational theory and experiment is used to refine the prediction of the third harmonic generation dispersion of C-76, and the two stable isomers of C-84 for which no experimental data are as yet available. We estimate that the two lowest lying resonances for C-76 and the two isomers of C-84 should occur slightly above 1500 and 1100 nm. A "missing state" scheme is used to identify the electronic states responsible for the resonances. The two- and three-photon absorption spectra are also calculated. Further comparison of the calculated gamma(-3 omega; omega, omega, omega) dispersion with the two- and three-photon simulated spectra together with the calculated gamma(-2 omega; 0, omega, omega) dispersion allows one to fully ascertain the nature of the resonances. The simple picture based on the SOS model limited only to the resonant states is found to account well for the response in the THG dispersion of C-60 Such a picture is nearly as successful for C70 but fails for higher fullerenes. A source of higher nonlinearity in C-60 is also explored. This is the possibility of the absorption to S-1 and its subsequent NLO response. The static, off-resonance, gamma(0; 0, 0, 0) for S-1 and S-2 is found to be an order of magnitude larger than that of S-0.