Vacancies are known to play an important role in the Hg-based narrow-gap alloys HgCdTe and HgZnTe. In this paper the authors summarise their recent calculations of the vacancy formation energies in HgCdTe and HgZnTe. They find that the vacancy formation energy in these alloys varies non-linearly with alloy concentration, resulting in higher vacancy densities than those predicted on the basis of a linear variation of the vacancy energies. Surface segregation in these alloys is driven by bond strength and bond length differences. They review their recent calculations which show that the chemical terms dominate in HgCdTe and result in Hg-rich surfaces, while in HgZnTe the strain terms contribute as well and result in a less Hg-rich surface, suggesting that HgZnTe surfaces may be more amenable to surface processes such as passivation.