The authors consider a model of the Hall effect when a quantum well (QW) with a parabolic potential V (z) = mWz2/2 (wherem and Wz are the effective mass of electron and the confinement frequency of QW, respectively) is subjected to a crossed dc electric field (EF) El = (E1: 0,0) and magnetic field B = (0. 0. B) in the presence of a strong electromagnetic wave (EMW) characterized by electric field E = (0, Eo sin (nt) .0) (where Eo and n are the amplitude and the frequency of the EMW, respectively). By using the quantum kinetic equation for electrons and considering the electro-optical phonon interFlction, the authors obtain analytical expressions for the conductivity as well as the Hall .coefficient (HC) with a dependence on B, E1, E0, n, the temperature T of the system and the characteristic parameters of QW. The analytical results are computationally evaluated and graphically plotted for a specific quantum well, GaAs/AlGaAs. Numerical results for the conductivity component Oxx show the resonant peaks which can be explained by the magnetophonon resonance and optically detected magnetophonon resonance conditions. Also, the HC reaches saturation as the magnetic field or the EMW frequency increases and weakly depends on the amplitude of the EMW. Furthermore, the HC in this study is always negative while it has both negative and positive values in the case of in-plane magnetic field.