  We have constructed fully self-consistent models of triaxial galaxies with
central density cusps. The triaxial generalizations of Dehnen's spherical
models are presented, which have densities that vary as 1/r^gamma near the
center and 1/r^4 at large radii. We computed libraries of about 7000 orbits in
each of two triaxial models with gamma=1 (weak cusp) and gamma=2 (strong cusp);
these two models have density profiles similar to those of the core and
power-law galaxies observed by HST. Both mass models have short-to-long axis
ratios of 1:2 and are maximally triaxial. A large fraction of the orbits in
both model potentials are stochastic, as evidenced by their non-zero Liapunov
exponents. We show that most of the stochastic orbits in the strong- cusp
potential diffuse relatively quickly through their allowed phase-space volumes,
on time scales of 100 - 1000 dynamical times. Stochastic orbits in the
weak-cusp potential diffuse more slowly, often retaining their box-like shapes
for 1000 dynamical times or longer. Attempts to construct self- consistent
solutions using just the regular orbits failed for both mass models.
Quasi-equilibrium solutions that include the stochastic orbits exist for both
models; however, real galaxies constructed in this way would evolve near the
center due to the continued mixing of the stochastic orbits. We attempted to
construct more nearly stationary models in which stochastic phase space was
uniformly populated at low energies. These ``fully mixed'' solutions were found
to exist only for the weak-cusp potential. No significant fraction of the mass
could be placed on fully-mixed stochastic orbits in the strong-cusp model,
demonstrating that strong triaxiality can be inconsistent with a high central
density.
