We present a globally integrated substorm (GIS) model in which the patchy-bursty tail reconnection process at ~20--35 RE and the magnetosphere-ionosphere (M-I) coupling process form a global feedback system to cause substorms. We identify the necessary and sufficient conditions for the expansion onset in the near-Earth plasma sheet. The necessary condition for substorm onset is an abrupt convection braking in the near-Earth plasma sheet at a rate ≥~3 (mV/m)/RE, which is equivalent to dipolarizing the tail-like field at a rate ≥~0.5 nT/s. The sufficient condition requires the disrupted tail current to be carried away by the Alfv¿n wave to form the substorm current wedge. These conditions must be satisfied by any onset mechanism. The Alfv¿n wave launched by the dipolarization-induced electric field must carry away the disrupted tail current from the dipolarization region. As an example, we show that substorm expansion onset can be triggered by abruptly braking a bursty bulk flow of ~3 mV/m within ~1 RE. The disrupted tail current at the expansion onset is ~105 A/RE carried away by the Alfv¿n wave launched by the dipolarization-induced electric field of ~14 mV/m. Substorm expansion onset in the ionosphere occurs ~1 min later when the Alfv¿n wave is reflected at the ionosphere. The dipolarization-induced tail reconnection and the M-I coupling form a feedback system to power the ongoing expansion phase which typically lasts ~30 min. As the dipolarizing region expands tailward, the expansion phase turns into recovery phase when the local tail current becomes too weak to sustain the expansion phase and the aurora activities start to retreat equatorward. ¿ 1998 American Geophysical Union