  We build a combinatorial invariant, called the spectral monodromy from the
spectrum of a non-selfadjoint h -pseudodifferential operator with two degrees
of freedom in the semi-classical limit. We treat small non-selfadjoint
perturbation of selfadjoint h-pseudodifferential operators in two case: in the
first, we assume that the classical flow of the unperturbed part is integrable;
the second case, more interesting, when this flow is assumed to be
quasi-integrable.
