The vibrational contributions to the Kerr effect and to electric-field-induced second-harmonic generation (ESHG) are calculated for methane for a number of optical frequencies. The latter results, together with the experimental ESHG values of the total mean second hyperpolarizability, allow for the determination of the omega(L)(2)-dispersion curve for the mean electronic hyperpolarizability. Since this curve is identical, to fourth order, for both processes, we are able to combine it with the calculated Kerr vibrational hyperpolarizabilities and predict the total Kerr hyperpolarizabilities for CH4 for several laser frequencies.