  We define hyperbolic groupoids, generalizing the notion of a Gromov
hyperbolic group. Examples of hyperbolic groupoids include actions of Gromov
hyperbolic groups on their boundaries, pseudogroups generated by expanding
self-coverings, natural pseudogroups acting on leaves of stable (or unstable)
foliation of an Anosov diffeomorphism, e.t.c.. We show that for every
hyperbolic groupoid G there is a naturally defined dual groupoid G' acting on
the Gromov boundary of a Cayley graph of G, which is also hyperbolic and such
that (G')' is equivalent to G.
