  We use both N-body simulations and integration in fixed potentials to explore
the stability and the long-term secular evolution of self-consistent,
equilibrium, non-rotating, triaxial spheroidal galactic models. More
specifically, we consider Dehnen models built with the Schwarzschild method. We
show that short-term stability depends on the degree of velocity anisotropy
(radially anisotropic models are subject to rapid development of radial-orbit
instability). Long-term stability, on the other hand, depends mainly on the
properties of the potential, and in particular, on whether it admits a
substantial fraction of strongly chaotic orbits. We show that in the case of a
weak density cusp (gamma=1 Dehnen model) the N-body model is remarkably stable,
while the strong-cusp (gamma=2) model exhibits substantial evolution of shape
away from triaxiality, which we attribute to the effect of chaotic diffusion of
orbits. The different behaviour of these two cases originates from the
different phase space structure of the potential; in the weak-cusp case there
exist numerous resonant orbit families that impede chaotic diffusion. We also
find that it is hardly possible to affect the rate of this evolution by
altering the fraction of chaotic orbits in the Schwarzschild model, which is
explained by the fact that the chaotic properties of an orbit are not preserved
by the N-body evolution. There are, however, parameters in Schwarzschild
modelling that do affect the stability of an N-body model, so we discuss the
recipes how to build a `good' Schwarzschild model.
