We have examined four well-defined events of sawtooth oscillations in energetic particle flux and magnetic field at geosynchronous orbit. During all four events, nearly simultaneous energetic particle flux enhancements and magnetic field variations occurred at all MLTs for each sawtooth cycle. Geomagnetic H component data at low to middle latitude also show a global H increase simultaneously with the geosynchronous responses at all MLTs, and the northern and southern PC indices generally show increases at each sawtooth cycle. All these are what is expected if solar wind pressure enhancements impacted the magnetosphere at times appropriate to have caused the onset of each sawtooth cycle. By directly checking the solar wind data, we find that there indeed exists a series of solar wind dynamic pressure enhancements for each sawtooth event. In identifying these pressure enhancements, we have found that the relative change in the dynamic pressure is important, particularly when the magnitude of the dynamic pressure is small and that even a modest dynamic pressure enhancement can result in significant changes in the magnetosphere when the IMF stays strongly southward for a long interval. We show that each cycle of the sawtooth oscillation can be reasonably associated in timing with a corresponding solar wind dynamic pressure enhancement. On the basis of this association and the global, simultaneous geosynchronous and ground responses, we suggest that the sawtooth oscillations studied in this paper are directly driven by series of solar wind pressure enhancements and are not a repetitive internal magnetospheric response to sustained enhanced solar wind energy input.