  We prove stability of the family of Kasner solutions within the class of
polarized $T^2$-symmetric solutions of the vacuum Einstein equations in the
contracting time direction with respect to an areal time foliation. All Kasner
solutions for which the asymptotic velocity parameter $K$ satisfies $|K-1|>2$
are non-linearly stable, and all sufficiently small perturbations exhibit
asymptotically velocity term dominated (AVTD) behavior and blow-up of the
Kretschmann scalar.
