Calculations of <(gamma)over bar>(-2 omega;omega,omega,0) for CH4 are reported for a number of frequencies(omega). This mean frequency-dependent second hyperpolarizability governs the nonlinear optical process: dc-electric-field-induced second-harmonic generation. Two levels of calculation have been carried out: one is based on the random phase approximation and the other on the multiconfigurational random phase approximation using a complete active space self-consistent-field wavefunction. This is the first calculation of <(gamma)over bar>(-2 omega;omega,omega,0) that has been made for CH4 using electron-correlated wavefunctions. Included in the calculations are corrections for vibrational effects of which the zero-point vibrational-averaging correction is both dominant and significant (13-18% of the electronic values). Comparison with experiment shows that not all the electron correlation is captured by our treatment. The dispersion properties are also discussed. (C) 1997 American Institute of Physics. [S0021-9606(97)02244-7].