  We prove that, for a finitely generated group hyperbolic relative to
virtually abelian subgroups, the generalised word problem for a parabolic
subgroup is the language of a real-time Turing machine. Then, for a hyperbolic
group, we show that the generalised word problem for a quasiconvex subgroup is
a real-time language under either of two additional hypotheses on the subgroup.
  By extending the Muller-Schupp theorem we show that the generalised word
problem for a finitely generated subgroup of a finitely generated virtually
free group is context-free. Conversely, we prove that a hyperbolic group must
be virtually free if it has a torsion-free quasiconvex subgroup of infinite
index with context-free generalised word problem.
