  Using $N$-body simulations ($N\sim 10^6 - 10^7$), we examine how a
non-axisymmetric dark halo affects the dynamical evolution of the structure in
collisionless (stellar) discs. We demonstrate how the model parameters such as
mass of the halo, initial conditions in the disc and the halo axes ratio affect
morphology and kinematics of the stellar discs. We show that a non-axisymmetric
halo can generate a large-scale spiral density pattern in the embedded stellar
disc. The pattern is observed in the disc for many periods of its revolution,
even if the disc is gravitationally over-stable. The growth of the spiral arms
is not accompanied by significant dynamical heating of the disc, irrelevant to
its initial parameters. We also investigate transformation of the dark halo's
shape driven by the long-lived spiral pattern in the disc . We show that the
analysis of the velocity field in the stellar disc and in the spiral pattern
gives us a possibility to figure out the spatial orientation of the
triaxial-shaped dark halo and to measure the triaxiality.
