A model for unsteady interactions between solar wind disturbances and the magnetosphere associated with the southward shift of the solar wind magnetic field during the growth phase of substorms is presented. It is emphasized that the presence of the solar wind electric current relating to the southward turning of the magnetic field and its interaction with the magnetosphere are essential in describing the transient process that generates the large-scale magnetospheric convection. Conceptual discussion on the stress generation due to the interaction in the outermost part of the magnetosphere and its transport into the inner magnetosphere and the high-latitude ionosphere are given. In comparison with the fast transient process, for instance, scc* of magnetic storms, the slow magnetosonic wave will play an essential role in the slow process, such as the early stage of the growth phase. By using the equivalent circuit model along with the above consideration the time response of the magnetosphere-ionosphere current system for this interaction is examined. The results indicate that a coupling of a rather large capacitance for the slow mode, in comparison with that for the Alfv¿n mode, with the ionospheric resistance can yield a long time delay for the saturation of the ionospheric current.