The relationship between a series of Pi2 pulsations and their associated substorm onsets with the IMF is examined on 5 May 1999. The magnetograms from the CANOPUS array show the occurrence of three substorm onsets, accompanied by Pi2 bursts. Analysis of the auroral electrojet location and current intensity as deduced from the Churchill line in the CANOPUS array shows that the following onsets move poleward. ACE and Wind magnetic field data show that the first onset occurs during a period of weak southward interplanetary magnetic field (IMF) and that the second onset occurs about an hour later when the IMF has become slightly northward. The third onset occurs during strongly northward IMF. Magnetic disturbances at GOES 8 and GOES 10 confirm that each onset is accompanied by disturbances in the field like those expected from the substorm current wedge. Meanwhile, from the IMP 8 observations in the magnetotail, the decreases of the total and X components of the magnetic field imply that significant removal of magnetic flux from the tail has occurred after the third onset. Thus a single cycle of dayside reconnection transport of open flux and reconnection of that open flux may contain within it multiple onsets of tail reconnection and dipolarization of the night magnetosphere, some possibly not involving the open flux in the lobes.