The phase stability of bcc-like NiAl and Ni2Al with respect to phase transformations into the ω phase is examined by first-principles, full-potential, linear muffin-tin orbital method (FPLMTO), band-structure calculations. In agreement with experiment we find that bcc-like NiAl is stable, whereas Ni2Al is unstable. We have also performed some calculations in slightly disordered phases, and find that the disordering tends to inhibit the transformation. This supports the suggestion that a combined displacive/ordering transformation mechanism is involved in the phase transformations of the Ni2Al system. Calculated lattice parameters and the degree of internal shuffling of atoms for the ordered Ni2Al phase were found to be in excellent agreement with the experiment.