  In this paper, we describe Bohr-Sommerfeld rules for semi-classical
completely integrable systems with 2 degrees of freedom with non degenerate
singularities (Morse-Bott singularities) under the assumption that the energy
level of the first Hamiltonian is non singular. The more singular case of {\it
focus-focus} singularities is studied in [Vu Ngoc San, CPAM 2000] and [Vu Ngoc
San, PhD 1998] The case of 1 degree of freedom has been studied in [Colin de
Verdiere-Parisse, CMP 1999] Our theory is applied to some famous examples: the
geodesics of the ellipsoid, the $1:2$-resonance, and Schroedinger operators on
the sphere $S^2$. A numerical test shows that the semiclassical Bohr-Sommerfeld
rules match very accurately the ``purely quantum'' computations.
