Trajectories of electrons with energies of 10--2000 MeV were studied using Tsyganenko's global quantitative model of the magnetosphere. Results were compared with balloon observations of atmospheric, return albedo, and cosmic electrons made at Prince Albert on August 26, 1987. Active geomagnetic conditions were associated with unusual variations in the flux of electrons on that date, which we interpret as a manifestation of an anomalously low and highly variable geomagnetic cutoff. Increasing the ring current intensity in the Tsyganenko model reduces the calculated effective cutoff rigidity somewhat, but to explain all of our observations, we must postulate that trajectories traditionally assumed to be forbidden are sometimes systematically converted into allowed trajectories. Within this model we can also identify field lines on which bursts of auroral X rays were generated. ¿ American Geophysical Union 1995