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Electron holes are a solitary wave of BGK type. Interest in such structures is due to the fact, that they may contribute to plasma heating and provide anomalous resistivity in various space plasma regions. Multisatellite space observations of electron holes have firmly established that these structures can have speeds comparable to ion thermal velocity. This fact presents a sort of an obstacle since the established theory of electron holes based on the assumption that ions are not perturbated. In our work we elaborate a model that adjusts the classical one by taking ion response into account. Based on measurements aboard MMS spacecraft, we found a homogeneous cluster of electron holes in the Earth’s plasma sheet. We show that background ion VDFs have a pronounced double-humped shape with electron hole speeds clustered near the local minimum. We elaborate a way to integrate the ion response into the BGK procedure thus obtaining a model that comprehensively takes ion response into account. In the frame of this model, we obtain new parametric regions available for the structures and estimate the trapped electron population. The problems of stability and acceleration are discussed.