We present a combined experimental and theoretical study of interactions between two-dimensional electron gases (2DEGs) and terahertz (THz) free-electron lasers in the presence of quantizing magnetic fields. It is found both experimentally and theoretically that when an intense THz field and a quantizing magnetic field are applied simultaneously to a GaAs-based 2DEG in the Faraday geometry, a strong cyclotron resonance (CR) effect on top of the magnetophonon resonances can be observed by transport measurements at relatively high temperatures. With increasing radiation intensity and/or decreasing temperature, the peaks of the CR are broadened and split due to magnetophoton–phonon scattering.