We extract the shape of the stellar velocity ellipsoid as a function o
f radius in M87 from van der Marel's [MNRAS, 270, 271 (1994)] velocity
dispersion data. We include the gravitational force of a central blac
k hole with the mass quoted by Harms et al. [ApJ, 435, L35 (1994)]. Th
e kinematical data are corrected for the effects of seeing and instrum
ental blurring using a nonparametric algorithm. We find that the stell
ar motions in M87 are slightly radially anisotropic throughout the mai
n body of the galaxy, with sigma(r) approximate to 1.2 sigma(t). Howev
er, sigma(t) exceeds sigma(r) within the inner 1'' - 2'' by a statisti
cally significant amount. A number of models for the formation of nucl
ear black holes predict a tangential anisotropy in the stellar motions
, and our results provide evidence for such an effect in M87. (C) 1997
American Astronomical Society.