  We have investigated the scale-invariant solutions of the BBGKY equations for
spatial correlation functions of cosmological density fluctuations and the mean
relative peculiar velocity in the strongly nonlinear regime.
  It is found that the solutions for the mean relative physical velocity depend
on the three-point spatial correlation function and the skewness of the
velocity fields. We find that the stable condition in which the mean relative
physical velocity vanishes on the virialized regions is satisfied only under
the assumptions which Davis \& Peebles took in his paper. It is found, however,
that their assumptions may not be general in real.
  The power index of the two-point correlation function in the strongly
nonlinear regime depends on the mean relative peculiar velocity, the
three-point correlation function and the skewness. If the self-similar
solutions exist, the power index in the strongly nonlinear regime is related to
the power index of the initial power spectrum and its relation depends on the
three-point correlation function and the skewness through the mean relative
peculiar velocity.
  Furthermore it is found that the mean relative physical velocity should have
the values between 0 and the Hubble expanding velocity. When the mean relative
physical velocity equals to the Hubble expanding velocity, there might exist
self-similar solutions in which the power index of the two-point correlation
function in the strongly nonlinear regime is independent of the initial power
index $n$.
