On the basis of quantum-statistical theory, magnetophonon resonance effects associated with linear and nonlinear (high-electric-field) relaxive electron transport are studied in the crossed electric (F I I i) and magnetic (B II Β£) fields. The interaction between electrons and polar LO phonons is considered for scattering processes. Analytic calculations are carried out for the inverse relaxation time obtained from the imaginary part of the field-dependent irreducible electron-self-energy within the first Born approximation. An explicit expression for the transverse field-dependent (nonlinear) conductivity (Tx)F) defined in the Ohm's law form of nonlinear electric current expressed in terms of the field-dependent relaxation time is also obtained for the nondegenerate case. The divergence nature of the nonlinear electric current (and hence the electric-field-dependent magnetoconductivity) associated with electric-field-induced magnetophonon resonance is examined in detail. We have obtained the high-field magnetophonon resonance condition in terms of electric-and magnetic-field strengths, temperature, effective mass of the electron, and principal quantum number (i.e. Landau level indices) difference, explicitly.