  It has recently been discovered that the Galactic bulge is X-shaped, with the
two southern arms of the X both crossing the lines of sight at l=0 and |b|>4,
hence producing a double red clump (RC) in the bulge CMD. Dynamical models
predict the formation of X-shaped bulges, as extreme cases of boxy-peanut
bulges. However, since X-shaped bulges were known to be present only in
external galaxies, models have never been compared to 3D kinematical data for
individual stars. We study the orbital motion of Galactic bulge stars, in the
two arms of the X in the southern hemisphere. The goal is to provide
observational constraints to bulge formation models that predict the formation
of X-shapes through bar dynamical instabilities. Radial velocities have been
obtained for a sample of 454 bulge giants, roughly equally distributed between
the bright and faint RC, in a field at (l,b)=(0,-6). Proper motions were
derived for all RC stars in the same field by combining images from two epochs
obtained 11 years apart. The proper motions for the spectroscopic subsample are
analyzed taking into account the radial velocities and metallicities measured
from near-IR Calcium triplet lines, for a subsample of 352 stars. The radial
velocity distribution of stars in the bright RC, tracing the closer overdensity
of bulge stars, shows an excess of stars moving towards the Sun. Similarly, an
excess of stars receding from the Sun is seen in the far overdensity, traced by
faint RC stars. This is explained with the presence of stars on elongated
orbits, most likely streaming along the arms of the X-shaped bulge. Proper
motions for these stars are consistent with qualitative predictions of
dynamical models of peanut-shaped bulges. Surprisingly, stars on elongated
orbits have preferentially metal poor metallicities, while the metal rich ones,
in both overdensities, are preferentially found in more axysimmetric orbits.
