  For a class of non-selfadjoint h-pseudodifferential operators in dimension 2,
we determine all eigenvalues in an h-independent domain in the complex plane
and show that they are given by a Bohr-Sommerfeld quantization condition. No
complete integrability is assumed, and as a geometrical step in our proof, we
get a KAM-type theorem (without small divisors) in the complex domain.
