A systematic total-energy study has been performed on the ω-phase of transition-metal-aluminide-based alloys using first-principles electronic structure calculations. The calculated o-phase heat of formation for ω-phase against the electron per atom ratio e/a is found to show the same trends as the measured diffuse ω peak for alloys with values of e/a between 3·3 and 4·7. Moreover, we predict that the ω-phase is the most stable amongst competing metastable phases for NbAl. ω collapse studies show a strong correlation between this transformation and a mechanical instability in the related B2 alloys at low temperatures. A partial ω-type shuffle is also predicted for Ni2Al alloys with e/a values close to 7 in the B82 structure type. As a result of these calculations, we are now able to study the phase diagrams of structurally important ternary alloys such as Ti‒Al‒V of Ti‒Al‒Nb.