  We exhibit exact conformal field theory descriptions of SO(N) and Sp(N) pairs
of Seiberg-dual gauge theories within string theory. The N=1 gauge theories
with flavour are realized as low energy limits of the worldvolume theories on
D-branes in unoriented non-critical superstring backgrounds. These unoriented
backgrounds are obtained by constructing exact crosscap states in the
SL(2,R)/U(1) coset conformal field theory using the modular bootstrap method.
Seiberg duality is understood by studying the behaviour of the boundary and
crosscap states under monodromy in the closed string parameter space.
