We present periodic (~2 hour) magnetospheric and ionospheric oscillations observed with multiple space-based and ground-based instruments during the severe magnetic storm of 25 September 1998. Periodic particle injections were observed at geosynchronous orbit. Ground magnetometers registered very large, as high as 3000 nT, magnetic deviations in the nightside auroral zone. The Millstone Hill incoherent scatter radar at magnetic latitude 55¿ measured periodic enhancements of ionospheric eastward ion velocity from midnight to ~1000 MLT. The periodic variations in the magnetometers and Millstone Hill radar were well correlated with the magnetospheric particle injections. The observations are consistent with the occurrence of periodic magnetospheric substorms during a magnetic storm. During each substorm cycle the ionospheric auroral zone expanded to the latitude of the Millstone Hill radar, so the radar was periodically within the auroral zone and detected the auroral plasma return flows. After substorm activity stopped, the Millstone Hill radar measured near-noon in-phase periodic oscillations of the ionospheric F-region electron density and temperature, which may be due to particle precipitation from the ring current and/or plasmasphere into the midlatitude ionosphere. We suggest that magnetospheric substorms during magnetic storms have a cycle time of ~2 hours. The magnetosphere can sustain similar oscillations for several cycles even though the substorm activity has stopped. All the observed periodic variations in the geosynchronous particle injections, in the auroral magnetic deviations, and in the ionospheric ion velocity are related to the periodic magnetospheric substorms and oscillations.