Аннотация:The development of geomagnetic storms is controlled mainly by external heliospheric plasma and magnetic field parameters, which, in turn, are determined by conditions on the Sun. According to them there can be isolated, repeated, multiple, or turbulent disturbance of the magnetosphere. To reveal the statistics and external preconditioning of single and multiple perturbations of the magnetosphere, geomagnetic storms were analyzed using the extensive database APEV (http://dbserv.sinp.msu.ru/apev/index.html) during the 23rd cycle of solar activity, from which geomagnetic storms have been grouped in 227 events. Results are presented in histograms, graphs, tables, and empirical formulas for the total number of intensification in all events and depending on the different phases of development, the amplitude and duration of geomagnetic grouped storms. Most of geomagnetic storms are complex and characterized by the existence of one or more side-extrema before or after the main one. This is due mainly to the superposition of individual perturbations from the Sun, which closely following one another in the heliosphere, or the internal structure and dynamics of disturbances in the corona.