Transition-metal (TM) carbides are an important class of hard, protective coating materials; however, their brittleness often limits potential applications. We use density functional theory to investigate the possibility of improving ductility by forming pseudobinary cubic M1M2C alloys, for which M1 = Ti or V and M2 = W or Mo. The alloying elements are chosen based on previous results showing improved ductility of the corresponding pseudobinary nitride alloys with respect to their parent compounds. While commonly-used empirical criteria do not indicate enhanced ductility in the carbide alloys, calculated stress/strain curves along known slip systems, supported by electronic structure analyses, indicate ductile behavior for VMoC. As VMoC layers are sheared along the 11¯0 direction on {111} planes, the stress initially increases linearly up to a yield point where the accumulated stress is partially dissipated. With further increase in strain, the stress increases again until fracture occurs. A similar mechanical behavior is observed for the corresponding TM nitride VMoN, known to be a ductile ceramic material 1. Thus, our results show that VMoC is a TM carbide alloy which may be both hard and ductile, i.e. tough. Display omitted