  Suppose $G$ is a 1-ended finitely presented group that is hyperbolic relative
to ${\bf P}$ a finite collection of 1-ended finitely presented proper subgroups
of $G$. If the boundary $\partial (G,{\bf P})$ has no cut point, then $G$ is
known to have semistable fundamental group at $\infty$. We consider the more
general situation when $\partial (G,{\bf P})$ contains cut points. Our main
theorem states that if each $P\in {\bf P}$ has semistable fundamental group at
$\infty$, then $G$ has semistable fundamental group at $\infty$.
