  We first discuss two-body and chain regularization methods for direct N-body
simulations on HARP-2 and GRAPE-6. The former is used for accurate integration
of perturbed binaries and hierarchies, whereas the latter deals with strong
interactions involving binaries. Combined with a powerful stability criterion
for hierarchical systems, this versatile treatment provides an efficient way of
studying all dynamical processes in globular clusters containing a realistic
population of primordial binaries. These algorithms are also ideal for
modelling a variety of astrophysical effects, such as averaging over Kozai
cycles, tidal circularization, spin-orbit coupling and stellar collisions,
where well-defined elements are used to describe near-singular solutions. We
also describe a new time-transformed leapfrog scheme which has been developed
to deal with black-hole binaries in galactic centres. This formulation is valid
for large mass ratios and dominant two-body motions in a compact subsystem can
be treated accurately in the post-Newtonian approximation. This method has been
combined with the existing regularization algorithms into a new simulation code
NBODY7. Some preliminary results of a test problem illustrating possible
applications are presented.
