Abstract: This invention comprises a running gear for rail vehicles with at least three wheel sets housed in a bogey frame and at least one steering device that makes possible a transverse displacement of an end wheel set, wherein the bogey frame, seen in longitudinal direction, has several sections, wherein at least the frontmost section, seen in the direction of travel, in which the leading wheel set is arranged, is connected horizontally pivotable to a second, rigid section, characterized in that at least the frontmost section, seen in the direction of travel, of the bogey frame in which the leading wheel set is arranged is formed as a parallelogram that can be displaced transversely to the longitudinal axis of the bogey frame.