After reviewing briefly the theory of the gyroresonant interactions between a quasimonochromatic whistler-mode wave and energetic electrons trapped in the magnetosphere, we extend this theory to consider such interactions for a natural whistler arising from a lightning discharge in the Earth's atmosphere. It is shown that, near the equatorial plane of the magnetosphere, whistler components above the nose frequency can accelerate energetic electrons. This acceleration takes place when the gyroresonant electrons are trapped by the wave field. The acceleration rate in this regime is much greater than is stochastic acceleration in the untrapped regime. It is not accompanied by pitch angle scattering which characterizes the untrapped regime. For example, at L = 3, a gyroresonant electron with an energy of ~6 keV and a pitch angle of 45¿ could have its energy increased by ~24% to 7.4 keV and its pitch angle changed to 70¿ after a single interaction with a whistler whose frequency changes from 1/3 to 1/2 the equatorial gyrofrequency. Highly anisotropic distributions of van Allen radiation belt electrons with pancake pitch angle distributions can result from such an acceleration.