  A homogeneous sample of galaxy redshifts in the core regions (R < 0.5
h$^{-1}$ Mpc) of 12 clusters is used to measure the frequency of substructure
with different tests. In 50 % of the cases substructure is detected, a
frequency which agrees well with previous studies of cluster cores. Magnitude
information and rough morphological classes are also available for 80 % of the
sample, allowing us to confirm that bright galaxies (M < -22 mag) have a
significantly lower velocity dispersion than the rest. Elliptical galaxies are
the main responsibles for this luminosity segregation in velocity space,
whereas no segregation can be seen for spiral galaxies. Given the coincidence
of substructure and luminosity segregation, a cluster model with an old
population of ellipticals which are under the effect of dynamical friction in
each subcluster is thus favoured by these observations. Spiral galaxies seem to
be late arrivals, or are passing in front or behind the core of the cluster.
