  The asymptotic behavior of geometry near the boundary of maximal Cauchy
development is studied using a perturbative method, which at the zeroth order
reduces Einstein's equations to an exactly solvable set of
equations---Einstein's equations with all ``space" derivatives dropped. The
perturbative equations are solved to an {\em arbitrarily-high order} for the
cosmological spacetimes admitting constant-mean-curvature foliation that ends
in a crushing singularity, i..e., whose mean curvature blows up somewhere.
Using a ``new" set of dynamical variables (generalized Kasner variables)
restrictions on the initial data are found that make the zeroth-order term in
the expansion asymptotically dominant when approaching the crushing
singularity. The results obtained are in agreement with the first order results
of Belinskii, Lifshitz and Khalatnikov on general velocity-dominated
cosmological singularities, and, in addition, provide clearer geometrical
formulation.
