Both nonlinear dielectric relaxation and dynamic Kerr effect responses of an assembly of polar and anisotropically polarizable molecules acted on by strong superimposed external dc E-0 and ac E-1(t)=E-1 cos omega t electric fields are evaluated in the context of the rotational diffusion model in the noninertial limit. The relaxation functions f(n)(t) (the expectation value of the Legendre polynomials P-n), which are appropriate to describe these nonlinear relaxation phenomena, are calculated by expanding them as a Fourier series in the time domain. An infinite hierarchy of recurrence relations for these Fourier amplitudes of f(n)(t) is obtained, the solution of which is expressed in terms of an infinite matrix continued fraction, so allowing us to evaluate the dynamic characteristics of the electric polarization and birefringence. For a weak ac field, the results predicted by the theory are in complete agreement with previous solutions obtained by perturbation methods. The solutions for the particular cases, where only either permanent or induced dipole moments are taken into account, can easily be extracted from the general solution. Diagrams of the frequency behavior of the in-phase and out-of-phase components of the electric birefringence and polarization are presented showing pronounced nonlinear effects due to the high ac field.