  We consider the self-similar solutions associated with the critical behavior
observed in the gravitational collapse of spherically symmetric perfect fluids
with equation of state $p=\alpha\mu$. We identify for the first time the global
nature of these solutions and show that it is sensitive to the value of
$\alpha$. In particular, for $\alpha>0.28$, we show that the critical solution
is associated with a new class of asymptotically Minkowski self-similar
spacetimes. We discuss some of the implications of this for critical phenomena.
