  We have preliminary results on the parallelization of a Tree-Code for
evaluating gravitational forces in N-body astrophysical systems. For our Cray
T3D/CRAFT implementation, we have obtained an encouraging speed-up behavior,
which reaches a value of 37 with 64 processor elements (PEs). According to the
Amdahl'law, this means that about 99% of the code is actually parallelized. The
speed-up tests regarded the evaluation of the forces among N = 130,369
particles distributed scaling the actual distribution of a sample of galaxies
seen in the Northern sky hemisphere. Parallelization of the time integration of
the trajectories, which has not yet been taken into account, is both easier to
implement and not as fundamental.
