  We have compiled a sample of 67 nearby ($z$ < 0.15) clusters of galaxies, for
which on average more than 150 spectroscopic members are available, and, by
applying different methods to detect substructures in their galaxy
distribution, we have studied their assembly history. Our analysis confirms
that substructures are present in 70% of our sample, having a significant
dynamical impact in 57% of them. A classification of the assembly state of the
clusters based on the dynamical significance of their substructures is
proposed. In 19% of our clusters, the originally identified brightest cluster
galaxy is not the central gravitationally dominant galaxy (CDG), but turns out
to be either the second-rank, or the dominant galaxy of a substructure (a SDG,
in our classification), or even a possible "fossil" galaxy in the periphery of
the cluster. Moreover, no correlation was found in general between the
projected offset of the CDG from the X-ray peak and its peculiar velocity. The
comparison of the CDGs properties with the assembly states and dynamical state
of the intracluster media, especially the core cooling status, suggests a
complex assembly history, with clear evidence of co-evolution of the CDG and
its host cluster in the innermost regions.
