  We use expansion-normalised variables to investigate the Bianchi type VII$_0$
model with a tilted $\gamma$-law perfect fluid. We emphasize the late-time
asymptotic dynamical behaviour of the models and determine their asymptotic
states. Unlike the other Bianchi models of solvable type, the type VII$_0$
state space is unbounded. Consequently we show that, for a general
non-inflationary perfect fluid, one of the curvature variables diverges at late
times, which implies that the type VII$_0$ model is not asymptotically
self-similar to the future. Regarding the tilt velocity, we show that for
fluids with $\gamma<4/3$ (which includes the important case of dust,
$\gamma=1$) the tilt velocity tends to zero at late times, while for a
radiation fluid, $\gamma=4/3$, the fluid is tilted and its vorticity is
dynamically significant at late times. For fluids stiffer than radiation
($\gamma>4/3$), the future asymptotic state is an extremely tilted spacetime
with vorticity.
