We present a study of the stability of stellar dynamical equilibrium models for M32. Kinematical observations show that M32 has a central dark mass $\sim 3 \times 10^6 \Msun$, most likely a black hole, 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 are sometimes bar-unstable. We have performed N-body simulations to test whether this the case for M32. This is the first stability analysis of two-integral models that have both a central density cusp and a nuclear black hole. Particle realizations with $N=512\,000$ were generated from distribution functions that fit the photometric and kinematic data of M32. We constructed equal-mass particle realizations and realizations with a mass spectrum to improve the central resolution. Models were studied for two inclinations, $i=90^{\circ}$ (edge-on) and $i=55^{\circ}$. The time evolution of the models was calculated with an implementation of a `self-consistent field code' on a Cray T3D parallel supercomputer. We find both models to be completely 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. A recent study by Sellwood \& Valluri suggests that for two-integral models, the bar-instability in flattened, rapidly rotating models is the only significantly unstable mode that affects systems rounder than $\sim$E7. Since M32 is one of the most rapidly rotating elliptical galaxies, it is likely that all two-integral models for real elliptical galaxies will generally be stable, except possibly for the case of very extreme inclinations.
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