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Strong disturbances of the Earth’s magnetic field (geomagnetic storms) may have significant effect upon operation of engineering devices and well-being of people. Therefore, prediction of the state of magnetosphere is a very important problem. Geomagnetic disturbances (GD) are one of important factors of space weather. In this study, we suggest an algorithm for objective discrimination of boundaries and different phases of GD based on the time series of hourly values of Dst geomagnetic index. Two or three phases were marked for each GD: initial phase (optional), main phase, and recovery phase. With the help of the suggested algorithm, the boundaries of GDs and their phases for the period from November 1997 till March 2014 have been marked automatically in an objective way. Then all the discovered GDs from 2010 till March 2014 were manually divided into three groups depending on the mechanism of their origin. In this study, the following physical phenomena were considered as the main GD sources: 1) coronal mass ejections (CME), connected as a rule with solar flares, and causing sporadic GD upon reaching the Earth’s orbit; 2) quasi-stationary high-speed streams of solar wind (SW) from coronal holes, responsible for recurrent GDs; 3) turn of the z-component of interplanetary magnetic field (IMF) towards south, resulting in the SW energy being freely injected into the Earth’s magnetosphere. Note that existence of negative (southward) Bz for a sufficiently long time is a necessary condition for a GD. Then, neural network prediction of the value of Dst index by the parameters of SW and IMF in L1 point and by preceding values of Dst index itself, has been performed. Prediction results and efficiency were compared for different GD phases and different types of GD origin. In this study, we perform detailed analysis of the obtained results, and suggest ways of improving existing approaches to neural network prediction of GDs with account for possible types of GD origin.