  We present a new dynamical model describing 3D motion in non axially
symmetric galaxies. The model covers a wide range of galaxies from a disk
system to an elliptical galaxy by suitably choosing the dynamical parameters.
We study the regular and chaotic character of orbits in the model and try to
connect the degree of chaos with the parameter describing the deviation of the
system from axial symmetry. In order to obtain this, we use the Smaller
ALingment Index (SALI) technique by numerically integrating the basic equations
of motion, as well as the variational equations for extensive samples of
orbits. Our results suggest, that the influence of the deviation parameter on
the portion of chaotic orbits strongly depends on the vertical distance $z$
from the galactic plane of the orbits. Using different sets of initial
conditions, we show that the chaotic motion is dominant in galaxy models with
low values of $z$, while in the case of stars with large values of $z$ the
regular motion is more abundant, both in elliptical and disk galaxy models.
