The dependence of the zonal geomagnetic indices (AE, Ap, Kp, Kn, and Dst) on the solar wind parameters (the electric field Ey component, dynamic pressure Pd and IMF irregularity σB) has been studied for two types of events: magnetic clouds and high-speed streams. Based on the empirical relationships, it has been established that the AE, Ap, Kp, and Kn indices are directly proportional to the Ey value at Ey < 12 mV m−1 and are inversely proportional to this value at Ey > 12 mV m−1 for the first-type events. On the contrary, the dependence of Dst on Ey is monotonous nonlinear. A linear dependence of all geomagnetic indices on Ey is typical of the second-type events. It has been indicated that the specific features of geoeffectiveness of magnetic clouds and high-speed solar wind streams are caused by the dependence of the electric field potential across the polar cap on the electric field, solar wind dynamic pressure, and IMF fluctuations.