A comprehensive experimental study is made of the magneto-optic absorption of Bi in the Voigt configuration in quantizing magnetic fields at frequencies covering the far-infrared range. At these frequencies, the typical magnetoplasma absorption features (cyclotron resonances, hybrid resonances and dielectric anomalies) gradually change character due to the strong quantization of the charge carrier system and because the experimental- and cyclotron frequency become comparable to - and finally exceed - the plasma frequency. The fundamental quantum cyclotron resonance lineshape becomes strongly affected by transitions with k B ≠ 0 ( k B momentum along magnetic field), due to the nonparabolic band structure. Effects of carrier redistribution over different carrier pockets in the quantizing field region are strongly reflected in the hybrid resonance and dielectric anomaly lineshapes. In order to analyze the data, the absorption spectra are calculated in the limit of local electrodynamics, using either a convensional classical method or more appropriate quantum-mechanical model. The latter model accounts qualitatively well for all major effects observed experimentally, taking into account the proper expression for the velocity matrix element for a nonparabolic band of the two-band model, over the entire frequency range. Nonlocal effects, clearly seen in the experimental data, are discussed qualitatively; these effects are illustrated by some additional experimental results obtained for Sb where nonlocal effects are very pronounced and strong.