  We study the formation of dark halos in a $\Lambda$CDM universe under the
assumption that Cold Dark Matter particles have a finite cross-section for
elastic collisions. We compare evolution when CDM mean free paths are
comparable to halo sizes with the collisionless and fluid limits. We show that
a few collisions per particle per Hubble time at halo centre can substantially
affect the central density profile. Cross-sections an order of magnitude larger
produce sufficient relaxation for rich clusters to develop core radii in the
range 100-200 $h^{-1}$kpc. The structural evolution of halos is a competition
between collisional relaxation caused by individual particle interactions and
violent relaxation resulting from the infall and merging processes by which
clusters grow. Although our simulations concentrate on systems of cluster size,
we can scale our results to address the halo structure expected for dwarf
galaxies. We find that collision cross-sections sufficiently large to
significantly modify the cores of such galaxies produce cluster cores which are
too large and/or too round to be consistent with observation. Thus the simplest
model for self-interacting dark matter is unable to improve fits to published
dwarf galaxy rotation curves without violating other observational constraints.
