  The well-known self-similar solution for the two-point correlation function
of the density field is valid only in an Einstein-de Sitter universe. We
attempt to extend the solution for non-Einstein-de Sitter universes. For this
purpose we introduce an idea of quasi-self-similar evolution; this approach is
based on the assumption that the evolution of the two-point correlation is a
succession of stages of evolution, each of which spans a short enough period to
be considered approximately self-similar. In addition we assume that clustering
is stable on scales where a physically motivated `virialization condition' is
satisfied. These assumptions lead to a definite prediction for the behavior of
the two-point correlation function in the strongly nonlinear regime. We show
that the prediction agrees well with N-body simulations in non-Einstein-de
Sitter cases, and discuss some remaining problems.
