The relationships between double-onset substorm, pseudobreakup, and IMF variation were investigated with magnetic, auroral, and particle observations from space to the ground during 0200--0600 UT on 4 September 1999. There were five consecutive bursts of Pi2 pulsations on the ground during the time of interest. The onset time of ground Pi2s maps to the same variation sequence in the IMF structure seen propagating to the Earth in multiple satellite observations in the upstream region. The comparison of auroral and energetic particle data with IMF observations shows that a sequence of two double-onset substorms intervened by a pseudobreakup appears in two distinct cycles of southward IMF followed by a northward interval. For the first substorm, the first onset begins when the By magnitude declines after the IMF turns southward for about 90 min, and the second onset occurs after northward turning of the IMF accompanied by an increasing By magnitude. The pseudobreakup appears while the IMF turns southward and the By magnitude slightly decreases. For the second substorm, the first onset commences while the IMF remains southward with a steady By magnitude, and the second onset occurs after the IMF becomes strongly northward and the By magnitude decreases instead. These observations can be explained with the two-neutral-point model. The first onset occurs when the IMF turns southward. Reconnection at the near-Earth neutral point first begins on closed field lines within the plasma sheet, and the second onset occurs when the IMF turns northward and reconnection at the distant neutral point ceases and reconnection at the near-Earth neutral point may reach the open flux of the tail lobes. In addition, a decrease in the By magnitude may help reduce magnetotail convection and release all the built-up flux to allow the onset to commence after northward turning of the IMF. If the IMF remains southward, the reduction of magnetotail convection due to a decreasing By would lead to a pseudobreakup instead. In contrast, an increasing By magnitude would increase magnetotail convection and weaken magnetospheric substorm after the IMF turns northward. Consequently, for the occurrence of double-onset substorms and pseudobreakups, not only the first onset begins spontaneously during steady southwardIMF and the second onset appears after northward turning of the IMF but the By change also affects magnetotail convection which may evoke (or abate) the substorm-related activation while the IMF turns southward (or northward).