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The nonlinear dielectric relaxation ac stationary response of an assembly of rigid polar molecules acted on by strong superimposed external dc E 0 and ac E 1 (t)= E 1 cos ω t electric fields is evaluated in the context of the noninertial rotational diffusion model. The calculation proceeds by expanding the relaxation functions f n (t)(the expectation value of the Legendre polynomials P n), which describe the nonlinear relaxation of the system, as a Fourier series in the time domain. Hence, an infinite hierarchy of recurrence equations for the Fourier components of f n (t) is obtained. The exact solution of this hierarchy can be obtained in terms of a matrix continued fraction, so allowing us to evaluate the ac nonlinear response. For a weak ac field our results are in complete agreement with previous solutions obtained by perturbation methods. Diagrams showing the behavior of the in-phase and out-of-phase components of …