  We present a detailed analysis of the velocity distribution and orientation
of orbits of subhaloes in high resolution cosmological simulations of dark
matter haloes. We find a trend for substructure to preferentially revolve in
the same direction as the sense of rotation of the host halo: there is an
excess of prograde satellite haloes. Throughout our suite of nine host haloes
(eight cluster sized objects and one galactic halo) there are on average 59% of
the satellites corotating with the host. Even when including satellites out to
five virial radii of the host, the signal still remains pointing out the
relation of the signal with the infall pattern of subhaloes. However, the
fraction of prograde satellites weakens to about 53% when observing the data
along a (random) line-of-sight and deriving the distributions in a way an
observer would infer them. This decrease in the observed prograde fraction has
its origin in the technique used by the observer to determine the sense of
rotation, which results in a possible misclassification of non-circular orbits.
We conclude that the existence of satellites on corotating orbits is another
prediction of the cold dark matter structure formation scenario, although there
will be difficulties to verify it observationally. Since the galactic halo
simulation gave the same result as the cluster-sized simulations, we assume
that the fraction of prograde orbits is independent of the scale of the system,
though more galactic simulations would be necessary to confirm this.
