The flux of relativistic electrons in geostationary orbit exhibits a variability closely regulated by the solar wind, but the acceleration mechanism of relativistic electrons remains poorly understood. Recent observational evidence has shown that the intensification of relativistic electrons often takes place in a matter of several hours. The rapidity is difficult to reconcile with traditional diffusion-based models which often take days to produce appropriate high-energy electron fluxes and motivates us to search for alternative mechanisms of internal acceleration. Elaborating on the observation in an earlier paper of Rostoker et al. [1998>, we propose that global oscillation of magnetosphere in the Pc4-5 range is capable of accelerating electrons under the catalysis of random pitch angle scattering. This view is developed theoretically and computationally in this paper. The most noteworthy result of the investigation is the demonstration that magnetic pumping by ULF waves can lead to the observed high relativistic electron flux in a time as short as a few hours under parameters appropriate for major magnetic storms. Further development and test of this theory are discussed. ¿ 1999 American Geophysical Union