  Compact object clusters are likely to exist in the centre of some galaxies
because of mass segregation. The high densities and velocities reached in them
deserves a better understanding. The formation of binaries and their subsequent
merging by gravitational radiation emission is important to the evolution of
such clusters. We address the evolution of such a system in a relativistic
regime. The recurrent mergers at high velocities create an object with a mass
much larger than the average. For this aim we modified the direct {\sc
Nbody6}++ code to include post-Newtonian effects to the force during two-body
encounters. We adjusted the equations of motion to include for the first time
the effects of both periastron shift and energy loss by emission of
gravitational waves and so to study the eventual decay and merger of radiating
binaries. The method employed allows us to give here an accurate post-Newtonian
description of the formation of a run-away compact object by successive mergers
with surrounding particles, as well as the distribution of characteristic
eccentricities in the events. This study should be envisaged as a first step
towards a detailed, accurate study of possible gravitational waves sources
thanks to the combination of the direct {\sc Nbody} numerical tool with the
implementation of post-Newtonian terms on it.
