Aims. We aim to study how the velocity segregation and the radial profile of the velocity dispersion depend on the prominence of the brightest cluster galaxies (BCGs). Methods. We divided a sample of 102 clusters and groups of galaxies into four bins of magnitude gap between the two brightest cluster members. We then computed the velocity segregation in bins of absolute and relative magnitude. Moreover, for each bin of magnitude gap we computed the radial profile of the velocity dispersion. Results. When using absolute magnitudes, the segregation in velocity is limited to the two brightest bins and no significant difference is found for different magnitude gaps. However, when we use relative magnitudes, a trend appears in the brightest bin:...