Models with f(E,L_z) and no central black hole cannot fit the observed central peak in the RMS line-of-sight velocity and the steep central rotation velocity gradient. A good fit to the data in the central arcsec is obtained when M32 is assumed to have a central black hole with mass M_BH = 1.8 x 10^6 solar masses. The major axis rotation velocity of M32 is approximately 90% of that of a maximally streaming f(E,L_z) model. Outside the central arcsec most of the data are remarkably well fitted by the f(E,L_z) models, with two exceptions. First, the even part of the observed major axis velocity profiles is slightly more flat-topped than that predicted by the models. Second, the models predict too much mean streaming on the intermediate axis (major +/- 45 degrees), relative to the major axis. So both the even and the odd part of the distribution function of M32 must in fact depend on a third integral of motion. Our models indicate that M32 most likely has a velocity distribution with [v_phi^2] > [v_theta^2] > [v_r^2] outside the central arcsec.
Our models are more realistic than most previous models in that they
take proper account of flattening, rotation and velocity profile
data. Yet, the models still require the presence of a massive central
black hole. To fit the M32 data without a black hole requires a
radially anisotropic velocity distribution in the central region and a
tangentially anisotropic velocity distribution in the outer
region. The measured excess of azimuthal motion outside the central
arcsec is not inconsistent with this picture. However, the required
excess of radial motion in the central region may be implausible,
given that the central two-body relaxation time in the absence of a
central black hole is a factor 10^2 shorter than the Hubble time.