  We show that near a focus-focus point in a Liouville integrable Hamiltonian
system with two degrees of freedom lines of locally constant rotation number in
the image of the energy-momentum map are spirals determined by the eigenvalue
of the equilibrium. From this representation of the rotation number we derive
that the twist condition for the isoenergetic KAM condition vanishes on a curve
in the image of the energy-momentum map that is transversal to the line of
constant energy. In contrast to this we also show that the frequency map is
non-degenerate for every point in a neighborhood of a focus-focus point.
