  We study the stability of stellar dynamical equilibrium models for M32.
Kinematic observations show that M32 has a central black hole of 3x10^6 solar
masses, and a phase-space distribution function that is close to the
`two-integral' form f=f(E,L_z). M32 is also rapidly rotating; 85-90% of the
stars have the same sense of rotation around the symmetry axis. Previous work
has shown that flattened, rapidly rotating two-integral models can be
bar-unstable. We have performed N-body simulations to test whether this is the
case for M32. Particle realizations with N=512,000 were studied for two
representative inclinations, i=90 (edge-on) and i=55, corresponding to
intrinsic axial ratios of q=0.73 and q=0.55, respectively. The time evolution
of the models was calculated with a `self-consistent field' code on a Cray T3D
parallel supercomputer. We find both models to be dynamically stable. This
implies that they provide a physically meaningful description of M32, and that
the inclination of M32 (and hence its intrinsic flattening) cannot be strongly
constrained through stability arguments.
  Previous work on the stability of f(E,L_z) models has shown that the bar-mode
is the only possibly unstable mode for systems rounder than q=0.3, and that the
likelihood for this mode to be unstable increases with flattening and rotation
rate. The f(E,L_z) models studied for M32 are stable, and M32 has a higher
rotation rate than nearly all other elliptical galaxies. This suggests that
f(E,L_z) models constructed to fit data for real elliptical galaxies will
generally be stable for q>0.55, and possibly for flatter systems as well.
