  N-body simulations argue that the inner haloes of barred galaxies should not
be spherical, nor even axisymmetric, but triaxial. The departure from
sphericity is strongest near the centre and decreases outwards; typical axial
ratios for the innermost parts are of the order of 0.8. The halo shape is
prolate-like in the inner parts up to a certain radius and then turns to
oblate-like. I call this inner halo structure the `halo bar' and analyse here
in depth its structure and kinematics in a representative model. It is always
considerably shorter than the disc bar. It lags the disc bar by only a few
degrees at all radii and the difference between the two bar phases increases
with distance from the centre. The two bars turn with roughly the same pattern
speed. This means that the halo bar is a slow bar, since its corotation radius
is much larger than its length. The bisymmetric component in the halo continues
well outside the halo bar in the form of an open spiral, trailing behind the
disc bar. The inner parts of the halo display some mean rotation in the same
sense as the disc rotation. This is more important for particles nearer to the
equatorial plane and decreases with increasing distance from it, but is always
much smaller than the disc rotation.
