The traditional picture of a carbon nanotube as a rolled graphene sheet implies that the mechanisms of intra-layer atomic processes in the two systems should be qualitatively similar. Using density-functional theory and tight-binding methods we show that the mechanism of single vacancy migration in nanotubes is different from that in graphite, as the curvature of the nanotube atomic network breaks the trigonal symmetry of a perfect graphene sheet, making the diffusion anisotropic, and strongly influencing the migration barrier. We further demonstrate that the formation energy of a double vacancy in nanotubes is smaller than that for a single vacancy, a behavior different from most monatomic solids, including graphite. (c) 2005 Elsevier B.V. All rights reserved.