  It is proposed that the odd-even staggering (OES) in the $\gamma$- bands of
heavy deformed nuclei can be reasonably characterized by a discrete
approximation of the fourth derivative of the odd-even energy difference as a
function of angular momentum $L$. This quantity exhibits a well developed
staggering pattern (zigzagging behavior with alternating signs) in rare earth
nuclei and actinides with long $\gamma$- bands ($L\geq 10$). It is shown that
the OES can be interpreted reasonably as the result of the interaction of the
$\gamma$ band with the ground band in the framework of a Vector Boson Model
with SU(3) dynamical symmetry. The model energy expression reproduces
successfully the staggering pattern in all considered nuclei up to $L=12-13$.
The general behavior of the OES effect in rotational regions is studied in
terms of the ground--$\gamma$ band-mixing interaction, showing that strong OES
effect occurs in regions with strong ground--$\gamma$ band-mixing interaction.
The approach used allows a detailed comparison of the OES in $\gamma$ bands
with the other kinds of staggering effects in nuclei and diatomic molecules.
