This paper examines the relationship between relativistic electron enhancements at geosynchronous orbit and magnetic storms measured by the Dst index. We analyzed the 30 most intense relativistic electron events from 1992 to 1995 and all events that occurred in 1993. Every relativistic electron event was associated with a magnetic storm in the Dst index, but, magnetic storms could occur with no appreciable enhancement of the relativistic electron fluxes. By correlating the maximum electron flux in each event with the minimum Dst value we found that the maximum relativistic electron fluxes and maximum ring current intensity are roughly correlated but that there is considerable variation. These results suggest that the solar wind conditions that are necessary to generate a ring current response are also necessary to generate a strong relativistic electron response but that there is some additional factor, either in the solar wind or in the magnetosphere, that determines whether a given storm will produce relativistic electrons or not and how strong that response will be.