The velocity field of galaxies in clusters is investigated on the basis of a sample consisting of 68 clusters with at least 30 galaxies for which redshifts are available in the literature; for 61 of these clusters, most of the galaxy magnitudes were collected. Galaxies brighter than the magnitude of the third-ranked object, m3, have velocities lower than average. These galaxies are preferentially located in the central regions. The effect is not induced by morphological segregation, it is not restricted to cD clusters, and it does not depend on the presence of substructures. The energy equipartition status seems to be achieved by these low-velocity galaxies. This evidence of segregation stresses the importance of m3 as a boundary between different dynamical statuses, and constrains the theory of structure and evolution of clusters of galaxies. A possible interpretation is given in terms of dynamical friction and merging