There has been considerable interest of late in the sudden appearance of large fluxes of relativistic electrons (E>1 MeV) at geostationary orbit due to the adverse effect these electrons can have on operational spacecraft. The question arises as to how these electrons are accelerated to relativistic energies in the relatively short time of a few hours. We shall show that large amplitude ULF pulsations are a unique feature of intervals of time in which the fluxes of relativistic electrons rise to high levels at radial distances beyond the normal L-shell range occupied by the outer radiation belt. We use SAMPEX polar orbiter data for the magnetic storm of November 1993 to show that the fluxes of E>400 keV electrons increase simultaneously over a broad range of L-shells and use this fact to suggest that large amplitude ULF pulsations have the potential to supply the energy necessary to create the relativistic electron fluxes. ¿ 1998 American Geophysical Union