Superluminous auroral kilometric radiation originates in the auroral cavity of the Earth's magnetosphere as right-hand extraordinary (R-X) mode emissions, with additional contributions from the left-hand ordinary (L-O) and left-hand extraordinary (L-X) modes. The three modes can propagate into the outer radiation belt and undergo gyroresonant interaction with trapped energetic electrons over a broad extent of the outer magnetosphere. We develop a general theory of quasi-linear diffusion and construct resonant diffusion curves in velocity space for each superluminous wave mode. The potential for stochastic electron acceleration is controlled by the dispersive properties of the waves and the ratio between the electron gyrofrequency and plasma frequency. It is found that each of the R-X, L-O, and L-X modes can produce significant acceleration of electrons over individual regions of parameter space. The L-O mode is found to have the potential for accelerating electrons from ~10 keV to ~MeV energies, over a broad range of wave normal angles, in spatial regions extending from the auroral cavity to the high-latitude (>30¿) outer radiation belt. The R-X mode appears to be less effective for accelerating magnetospheric electrons, since acceleration to significant energies (~MeV) requires very small wave normal angles (<10¿). The potential for significant electron acceleration in the magnetosphere by L-X mode waves is restricted not least by the requirement of high minimum energies, e.g., 400 keV in the outer radiation belt. To assess whether the superluminous wave modes contribute significantly to the stochastic acceleration of relativistic electrons during geomagnetic storms, the present study needs to be supplemented by ray-tracing analyses and the calculation of energy diffusion coefficients incorporating data on wave power. ¿ 2001 American Geophysical Union