  By combining galaxy tracers from high-resolution N-body and hydrodynamical
simulations, we present a consistent picture of the behaviour of galaxy
velocities in massive clusters. In haloes above ~ 10^14 Msun, the brightest
satellite galaxies are slightly cooler compared to the dark matter, while
fainter satellites are hotter. Within the virial radius of a cluster, the mean
velocity dispersion based on the 100 brightest galaxies is a factor of 1.065
+/- 0.005 (stat) +/- 0.027 (sys) higher than that of the dark matter
(corresponding to a ~10-15 per cent bias in the dynamical mass estimate) while
that based on only the five brightest galaxies is 0.868 +/- 0.039 (stat) +/-
0.035 (sys). These trends are approximately independent of redshift. The
velocity structure is sensitive to the modelling of galaxies in clusters,
indicative of the complex interplay of tidal stripping, dynamical friction, and
merging. Velocity dispersions derived from instantaneous subhalo properties are
larger than those employing either peak subhalo properties or hydrodynamical
galaxy tracers. The latter two methods are consistent, implying that stacked
spectroscopic analysis of cluster samples should, after correction for
projection, show a trend towards slightly higher velocities when fainter
galaxies are included, with an unbiased measure of dark matter velocity
dispersion coming from approximately 30 galaxies per cluster. We show evidence
that the velocity distribution function of bright galaxies near the cluster
centre has a low-velocity tail due to strong dynamical friction.
