In cases with a sufficiently strong bar in the disc component, the halo does not stay axisymmetric, but shows also a bar-like or oval deformation. An example can be seen in Fig. 2 of Holley-Bockelmann, Weinberg & Katz (2003; HBWK). I found such structures also in my own simulations and I call them, for simplicity, halo bars. Preliminary results show that, in cases with a strong disc bar, the halo bar is triaxial, but prolate like, with axial ratios of the order of 0.7 or 0.8 in the inner parts, and becomes more spherical as the radius increases. The length of the halo bar increases with time, but always stays considerably shorter than that of the disc bar. It is roughly aligned with the disc bar at all times (at least within the measuring errors), i.e. it turns with roughly the same pattern speed. This means that it is a slow bar. The bisymmetric component in the halo extends well beyond the end of the halo bar, and there it trails behind the disc bar, much as seen in Fig. 2 of HBWK. The properties of these halo bars will be discussed in detail elsewhere (Athanassoula, in prep.).