  We study the stability of trajectories near the disk plane of galaxy models
with a triaxial dark matter halo component. We also examine the effect of weak
discreteness noise, rapidly rotating bar perturbations and weak dissipation on
these trajectories. If the matter distribution is triaxial and has a constant
density core, dissipation leads to inflow of material inside the core radius to
the centre. This leads to the formation of central masses which in turn
destabilise the trajectories of any stars formed in these regions. In
particular, even if the gas settles by dissipation into a flat disk, stars
formed in that disk will later form a bulge like dstribution the extent of
which would be related to the core radius of the halo and the original
asymmetry in the plane. The process of gas inflow is regulated by the fact that
too large and condensed a central mass leads to the creation of stable closed
loop orbits in the central area around which the gas can move. This would
appear to stop the accumulation of central mass before it becomes large enough
for rapid loss of halo triaxiality. It was found that weak discreteness noise
can change the fraction of such trajectories significantly and can therefore
have important consequences for the modelling of galaxies. The addition of
rapidly rotating bar perturbations also increases the degree of instability
dramatically. So if bars can form in triaxial haloes they are likely to be
quickly destroyed leaving a bulge like structure behind (which may explain the
absence of bars in surveys of high redshift galaxies).
