  We discuss the performance of direct summation codes used in the simulation
of astrophysical stellar systems on highly distributed architectures. These
codes compute the gravitational interaction among stars in an exact way and
have an O(N^2) scaling with the number of particles. They can be applied to a
variety of astrophysical problems, like the evolution of star clusters, the
dynamics of black holes, the formation of planetary systems, and cosmological
simulations. The simulation of realistic star clusters with sufficiently high
accuracy cannot be performed on a single workstation but may be possible on
parallel computers or grids. We have implemented two parallel schemes for a
direct N-body code and we study their performance on general purpose parallel
computers and large computational grids. We present the results of timing
analyzes conducted on the different architectures and compare them with the
predictions from theoretical models. We conclude that the simulation of star
clusters with up to a million particles will be possible on large distributed
computers in the next decade. Simulating entire galaxies however will in
addition require new hybrid methods to speedup the calculation.
