  We consider the asymptotic behaviour of spatially homogeneous spacetimes of
Bianchi type IX close to the singularity (we also consider some of the other
Bianchi types, e. g. Bianchi VIII in the stiff fluid case). The matter content
is assumed to be an orthogonal perfect fluid with linear equation of state and
zero cosmological constant. In terms of the variables of Wainwright and Hsu, we
have the following results. In the stiff fluid case, the solution converges to
a point for all the Bianchi class A types. For the other matter models we
consider, the Bianchi IX solutions generically converge to an attractor
consisting of the closure of the vacuum type II orbits. Furthermore, we observe
that for all the Bianchi class A spacetimes, except those of vacuum Taub type,
a curvature invariant is unbounded in the incomplete directions of inextendible
causal geodesics.
