  We use Fuchsian Reduction to study the behavior near the singularity of a
class of solutions of Einstein's vacuum equations. These solutions admit two
commuting spacelike Killing fields like the Gowdy spacetimes, but their twist
does not vanish. The spacetimes are also polarized in the sense that one of the
`gravitational degrees of freedom' is turned off. Examining an analytic family
of solutions with the maximum number of arbitrary functions, we find that they
are all asymptotically velocity-term dominated as one approaches the
singularity.
