The dynamics of the intensity of cosmic rays is known to be different on the ascending and descending branches of the 11-year solar cycle, i.e., hysteresis phenomena are observed. Recently, it has been obtained that at shorter intervals on the scale of magnetic storms there are also signs of hysteresis in dependences of cosmic ray cutoff rigidities R (geomagnetic thresholds) on heliosphere and geosphere parameters. R is the rigidity below which a particle flux is cut off due to geomagnetic shielding. In this paper, we have analyzed the dependence of the geomagnetic storm index Dst and the variation of the ΔR thresholds on interplanetary magnetic field (IMF) and solar wind (SW) parameters during the two-step magnetic storm on September 7–8, 2017. We have found hysteresis phenomena in the following paired series: (1) dependences of Dst on SW and IMF parameters, and (2) dependences of ΔR on SW and IMF parameters. We have established that the dependence curves in the storm descending phase (main phase) and ascending phase (recovery phase) do not coincide — hysteresis loops are formed. A specific feature of the storm under study is the second lowering of Dst in the recovery phase. The hysteresis pattern reflects this specific storm dynamics, forming two hysteresis loops in response to the two Dst drops.