A method of calculation of the nonlinear transient response of an assembly of fixed axis (two-dimensional) rotators due to sudden changes of a strong external dc electric field is presented. The infinite hierarchy of differential-recurrence relations for the decay functions describing the relaxation of the system is derived by averaging the underlying inertial Langevin equation. The solution for the one-sided Fourier transform of this hierarchy is obtained in terms of matrix continued fractions. The integral relaxation time and the spectrum of the electric polarization for various kinds of nonlinear transient responses (step-on, step-off, rapidly rotating field) are calculated for typical values of the model parameters. Both exhibit pronounced nonlinear effects due to the strong dc field. Analytical equations for the quantities of interest are presented for particular cases (in the overdamped and low damping limits, etc.).