  We investigate the orbital structure in a class of 3D models of barred
galaxies. We consider different values of the pattern speed, of the strength of
the bar and of the parameters of the central bulge of the galactic model. The
morphology of the stable orbits in the bar region is associated with the degree
of folding of the x1-characteristic. This folding is larger for lower values of
the pattern speed. The elongation of rectangular-like orbits belonging to x1
and to x1-originated families depends mainly on the pattern speed. The detailed
investigation of the trees of bifurcating families in the various models shows
that major building blocks of 3D bars can be supplied by families initially
introduced as unstable in the system, but becoming stable at another energy
interval. In some models without radial and vertical 2:1 resonances we find,
except for the x1 and x1-originated families, also families related to the
z-axis orbits, which support the bar. Bifurcations of the x2 family can build a
secondary 3D bar along the minor axis of the main bar. This is favoured in the
slow rotating bar case.
