The stochastic mixing of protons in the energy range from 1 to 30 keV in the night-side magnetosphere is studied by calculating the local divergence rate of neighboring orbits and the two-time velocity correlation function. The rate of divergence of neighboring bundles of trajectories is shown to have large bursts with average separation times of order 1 minute per e-folding during the crossing of the central plasma sheet in the region beyond --50Re. For the Tsyganenko magnetosphere the net amount of orbit divergence is 15 to 20 e-foldings in one hour. The velocity correlations are shown to decay as power laws &tgr;-m with a distribution of m values. These results indicate that for short time (<1 hour) there is reversibility and memory for the protons but for longer times there is no memory for protons in the nightside magnetosphere. ¿American Geophysical Union 1991