The dominant interplanetary phenomena that are frequently associated with intense magnetic storms are the interplanetary manifestations of fast coronal mass ejections (CMEs). Two such interplanetary structures, involving an intense and long duration B s component of the IMF are: the sheath region behind a fast forward interplanetary shock, and the CME ejecta itself. Frequently, these structures lead to the development of intense storms with two-step growth in their main phases.These structures, when combined, lead sometimes to the development of very intense storms, especially when an additional interplanetary shock is found in the sheath plasma of the primary structure accompanying another stream. The second stream can also compress the primary cloud, intensifying the B s field, and bringing with it an additional B s structure. Thus, at times very intense storms are associated with three or more B s structures.Another aspect that can contribute to the development of very intense storms refers to the recent finding that magnetic clouds with very intense core magnetic fields tend to have large velocities, thus implying large amplitude interplanetary electric fields that can drive very intense magnetospheric energization.