  We discuss how the centres of galaxy clusters evolve in time, showing the
results of a series of direct N-body simulations. In particular, we followed
the evolution of a galaxy cluster with a mass $M_{clus} \simeq 10^{14}
$M$_{\odot}$ in different configurations. The dynamical evolution of the system
leads in all the cases to the formation of dense and massive sub-structures in
the cluster centre, that form in consequence of a series of collisions and
merging among galaxies travelling in the cluster core. We investigate how the
structural properties of the main merging product depends on the
characteristics of those galaxies that contributed to its formation.
