In this paper, we propose to study the magneto-photon-phonon resonance effects observed in terahertz (THz)-driven two-dimensional electron gases in strong magnetic fields. The photon energy of the THz electromagnetic radiations is on the scale of the cyclotron energy (induced by strong magnetic fields) and the LO-phonon energy so that (i) THz radiations will modify strongly the process of electron energy relaxation in the device structure; (ii) electrons can gain the energy from ac and dc driving fields through, e.g., absorption of the photons and lose the energy through, e.g., emission of the LO phonons; and (iii) resonant scattering will occur among different Landau levels (LL’s) when a condition Mωc+ω=ωLO is satisfied, where ωc (ω,ωLO) is the cyclotron (photon, LO phonon) frequency and M is an index difference between two LL’s. This leads to an enhancement of the resistivity and, consequently, to an enhanced rate of the absorption of the THz electromagnetic radiation in the sample systems. Varying the photon and cyclotron frequencies will result in a series of magneto-photon-phonon resonances observed in the dc resistivity (or conductivity) and/or in the optical absorption coefficient. We have presented a detailed theoretical study to observe this quantum resonance effect.