Recently it has been reported that osmium diboride has an unusually large bulk modulus combined with high hardness, and consequently is a most interesting candidate as an ultra-incompressible and hard material. The electronic and structural properties of the transition metal diborides OsB2 and RuB2 have been calculated within the local density approximation (LDA). It is shown that the high hardness is the result of covalent bonding between transition metal d states and boron p states in the orthorhombic structure. (c) 2006 Elsevier B.V. All rights reserved.