  We report on the detailed analysis of the mean-pairwise peculiar velocity
profile in high-resolution cosmological N-body simulations ($N=8.8\times 10^6$
particles in a sphere of $50 \sim 200$Mpc radius). In particular we examine the
validity and limitations of the stable condition which states that the mean
{\it physical} separation of particle pairs is constant on small scales. We
find a significant time-variation (irregular oscillatory behavior) of the
mean-pairwise peculiar velocity in nonlinear regimes. We argue that this
behavior is not due to any numerical artifact, but a natural consequence of the
continuous merging processes in the hierarchical clustering universe. While
such a time-variation is significant in a relatively local patch of the
universe, the global average over a huge spatial volume $\simgt$(200Mpc)$^3$
does not reveal any {\it systematic} departure from the stable condition. Thus
we conclude that the mean-pairwise peculiar velocity is rather unstable
statistics but still satisfies the stable condition when averaged over the
cosmological volume.
