  Hamiltonian Monodromy is the simplest topological obstruction to the
existence of global action-angle coordinates in a completely integrable system.
We show that this property can be studied in a neighborhood of a focus-focus
singularity by a spectral Lax pair approach. From the Lax pair, we derive a
Riemann surface which allows us to compute in a straightforward way the
corresponding Monodromy matrix. The general results are applied to the
Jaynes-Cummings model and the spherical pendulum.
