  We study the spectral problem of N=4 SYM with gauge group SO(N) and Sp(N). At
the planar level, the difference to the case of gauge group SU(N) is only due
to certain states being projected out, however at the non-planar level novel
effects appear: While 1/N-corrections in the SU(N) case are always associated
with splitting and joining of spin chains, this is not so for SO(N) and Sp(N).
Here the leading 1/N-corrections, which are due to non-orientable Feynman
diagrams in the field theory, originate from a term in the dilatation operator
which acts inside a single spin chain. This makes it possible to test for
integrability of the leading 1/N-corrections by standard (Bethe ansatz) means
and we carry out various such tests. For orthogonal and symplectic gauge group
the dual string theory lives on the orientifold AdS5xRP5. We discuss various
issues related to semi-classical strings on this background.
