In this paper we discuss the main-phase evolution of intense magnetic storms, associated with the passage of different interplanetary magnetic structures. It is shown that their evolution, driven by intense magnetic fields in the sheath region just behind interplanetary shocks, evolves faster (implying physically different magnetospheric configurations) than that associated with intense magnetic fields in the ejecta itself and in corotating streams. The estimated ring-current injection rate for the main phase of intense magnetic storms caused by sheath fields is ∼10 times greater than the estimated injection rate for N–S magnetic clouds. Based on these results, we propose storm-intensity criteria for several classes of the driving interplanetary structures. The time necessary to reach a Dst/SYM index threshold level is an important parameter for a space weather forecast.