An extended relativistic model is developed to evaluate the superluminous R-X-mode resonance especially the second-order and third-order resonances with electrons in the Earths magnetosphere. The potential for stochastic electron acceleration driven by the R-X mode is determined by the dispersive properties of the R-X mode and specifically the resonant harmonic N. In contrast to the limited acceleration at the first harmonic (N = 1)resonance, for the higher harmonic (N ＞ 1) resonances, the R-X mode is capable of accelerating electrons from ～10keV to ～ MeV energies, over a wide range of wave normal angles, in spatial regions extending from the auroral cavity to the latitude (＞30°) outer radiation belt. This indicates that higher-order resonance is essentially important for the electron acceleration for the oblique wave propagation.