  We present a detailed study, in the semi-classical regime $h \to 0$, of
microlocal properties of systems of two commuting h-PDO s $P_1(h)$, $P_2(h)$
such that the joint principal symbol $p=(p_1,p_2)$ has a special kind of
singularity called a "focus-focus" singularity. Typical examples include the
quantum spherical pendulum or the quantum Champagne bottle.
  In the spirit of Colin de Verdi\`ere and Parisse, we show that such systems
have a universal behavior described by singular quantization conditions of
Bohr-Sommerfeld type.
  These conditions are used to give a precise description of the joint spectrum
of such systems, including the phenomenon of quantum monodromy and different
formulations of the counting function for the joint eigenvalues close to the
singularity, in which a logarithm of the semi-classical constant $h$ appears.
Thanks to numerical computations done by M.S. Child for the case of the
Champagne bottle, we are able to accurately illustrate our statements.
