The frequency-dependent vibrational second hyperpolarizability of CH4-nFn molecules with n=0-4 has been computed for the most common nonlinear optical (NLO) processes by adopting the perturbation approach due to Bishop and Kirtman [J. Chem. Phys. 95, 2646 (1991)]. These calculations have been performed by using the Sadlej atomic basis set with the Hartree-Fock technique as well as with the Møller-Plesset second order perturbation theory (MP2) procedure. The inclusion of electron correlation and of the first-order mechanical and electrical anharmonicities turn out to be of quantitative importance for most quantities. In particular, it permits us to improve the agreement with the experimental data for the difference between the anisotropic dc-Kerr and mean electric-field-induced second harmonic generation (ESHG) vibrational second hyperpolarizability of CF4. With the exception of the small ESHG vibrational second hyperpolarizability the infinite optical frequency method turns out to be a satisfactory approximation for evaluating the vibrational NLO responses.