[en] The Langevin equations of motion of the cage model of polar liquids originally proposed by Hill (1963 Proc. Phys. Soc. 82 723) are solved for the first time for the particular case of rotation about a fixed axis, using a newly developed matrix continued fraction method. It is shown that the cage model predicts both the low-frequency Debye relaxation and a pronounced high-frequency (Poley) absorption peak in the far-infrared (FIR) region. The similarity of the equations of motion of the cage model to the equations which arise in the problem of generalizing the Onsager model of polar fluids to include a time-varying applied field suggests that the FIR (Poley) absorption may have its origins in the combined influence of molecular inertia and the torque due to the reaction field in the frequency-dependent version of the Onsager model. The complex susceptibility yielded by the cage model is shown to be in good agreement with experimental data on CH₃Cl that were taken as a typical example. Moreover, a simple approximate formula based on a small-oscillation approximation can describe accurately the dielectric spectra in most cases of interest