The stabilities of (BN) x (C 2 ) 1-x alloys and related superlattices are investigated by ab initio pseudopotential calculations. We find that the (BN) 1 /(C 2 ) 1 superlattices in (111) orientations have the lowest formation energy among many short-range ordered BNC 2 structures due to the smallest number of B-C and C-N bonds. Based on the calculated formation energies at several compositions and for various ordered structures and assuming thermodynamic equilibrium, the solid solution phase diagram of (BN) x (C 2 ) 1-x alloys is constructed. We find that the complete miscibility of (BN) x (C 2 ) 1-x alloys is possible, which is in contrast with previous theoretical predictions but in agreement with experimental reports. Key words: Density functional theory, diamond, boron nitride, alloy, superlattice, stability, miscibility.There has recently been considerable interest in new B-C-N ternary compounds that have potential uses as superhard materials and electrical materials. Since diamond and cubic BN are well-known materials with the highest hardness, cubic BCN compounds are expected to exhibit excellent mechanical properties and high hardness. Such cubic ternary B-C-N systems are also expected to be thermally and chemically more stable than diamond. They should also be wide band gap semiconductors since diamond and c-BN have band gaps of 5.5 eV and 6.1 eV respectively.Although there have been a few reports on the synthesis of cubic B-C-N (c-BCN) materials, several outstanding issues remain. For example, Badzian 1 reported the synthesis of (BN) x (C 2 ) 1-x solid solutions, where 0.15