The nonlinear effects arising from the first and second hyperpolarizabilities on the Kerr effect relaxation response of an ensemble of polar and anisotropically polarizable molecules in a strong de electric field are studied by solving the infinite hierarchy of differential-recurrence relations underlying the noninertial Fokker-Planck (Smoluchowski) equation. The step-on solution is obtained by using the matrix continued fraction methods. An expression for the Kerr effect relaxation time is derived as well following the procedure of Kalmykov, Dejardin, and Coffey [Phys. Rev. E 55, 2509 (1997)] which is in full agreement with the matrix continued fraction expression. For small values of the electric held, it is shown that the first hyperpolarizability contributes to increasing the Kerr effect relaxation time while the second hyperpolarizability shifts the maximum of the relaxation time toward the lowest electric fields on increasing the value of this maximum. The dual nature of essentially two relaxation processes is also emphasized by plotting the Kerr effect relaxation spectra for various values of the first and second hyperpolarizability parameters.