  Solvability of the conjugacy problem for relatively hyperbolic groups was
announced by Gromov [Hyperbolic groups, MSRI publications 8 (1987)]. Using the
definition of Farb of a relatively hyperbolic group in the strong sense [B
Farb, Relatively hyperbolic groups, Geom. Func. Anal. 8 (1998) 810-840], we
prove this assertion. We conclude that the conjugacy problem is solvable for
fundamental groups of complete, finite-volume, negatively curved manifolds, and
for finitely generated fully residually free groups.
