AbstractDuring southward interplanetary magnetic field (IMF) conditions, the subsolar magnetopause moves inward even under steady solar wind pressure. This is generally referred to as “erosion.” Empirical and computational studies have been conducted to quantify the effect of magnetopause erosion; however, they generally use steady state IMF conditions. Solar wind conditions are not usually constant for very long, especially during such conditions as are present in high‐speed streams, which typically have large fluctuations in the IMF. These IMF fluctuations can occur on a range of times scales and amplitudes, resulting in a series of northward and southward IMF intervals imposed on the magnetosphere. We have simulated the effect of such IMF variations on the magnetopause position using a global magnetohydrodynamic model. We find that there are both time lag and hysteresis‐like effects on the motion of the magnetopause due to the variation in the magnitude of the southward IMF and that the instantaneous position of the magnetopause can be significantly different from what one would expect from steady state conditions.