  The goal of this paper is to find the quantization conditions of
Bohr-Sommerfeld of k quantum Hamiltonians acting on the euclidian space of
dimension n, depending on a small parameter h, and which commute to each other.
That is we determine, around a regular energy level E of the euclidian space of
dimension k the principal term of the asymptotics in h of the eigenvalues of
the operators that are associated to a common eigenfunction. Thus we localize
the so-called joint spectrum of the operators.
  Under the assumption that the classical Hamiltonian flow of the joint
principal symbol is periodic with constant periods on the energy level of E(a
submanifold of codimension k) we prove that the part of the joint spectrum
lying in a small neighbourhood of E is localized near a lattice of size h
determined in terms of actions and Maslov indices. The multiplicity of the
spectrum is also determined.
