Number density and temperature of cold H+ ion fluxes in the plasmasphere measured by the Auroral probe/Alpha 3 experiment during two geomagnetic storms are analyzed. It was found that after the onset of geomagnetic storms the plasmapause both on the night and day sides starts moving toward the Earth almost simultaneously. The delay of the beginning of plasmapause movement on the day side relative to the night side is at least much less than the corotation time of magnetic tube with cold plasma from the night sector into the day sector of the plasmasphere. It was found that the number density of cold plasma inside the daytime plasmasphere could significantly change, either decrease or increase, during moderate geomagnetic storms. Now we cannot definitely determine the reason for these variations, but we assume they are caused by variations of parameters (e.g., nmaxF2,hmaxF2) in the underlying ionosphere initiated by geomagnetic storms.