  Space-based observations are beginning to yield detailed information about
the stellar kinematics at the very centers of galaxies, within the sphere of
gravitational influence of the black hole. The structure and dynamics of these
regions is probably determined in part by the infall and coalescence of black
holes during galaxy mergers. A goal of N-body simulations is to reproduce the
kinematics near the black holes as well as the relations that exist between the
nuclear and global properties of galaxies. However, the problem is
computationally difficult due to the wide range of length and time scales, and
no single N-body code can efficiently follow the evolution from kiloparsec to
sub-parsec scales. We review existing N-body work on this problem and present
the first, fully self-consistent merger simulations of galaxies containing
dense stellar cusps and black holes.
