New spin-polarized total-energy band calculations employing the augmented-spherical-wave method and the fixed-spin-moment procedure are used to study the volume and pressure dependence of the magnetic properties of Ni3Al in the Cu3Au crystal structure. Energy minimization is used to find the ratio of the equivalent aluminum and nickel sphere radii, the stable nonmagnetic and magnetic solutions, and the equilibrium volume. The ratio of the sphere radii is found to be 1.08, and a weak first-order transition from nonmagnetic to ferromagnetic behavior is found at a lattice constant 0.7% below the zero-pressure equilibrium lattice constant of 6.704 a.u. (3.73). The magnetic moment and its pressure dependence at equilibrium are found to be 0.34 B/cell and -0.40(B/atom)/Mbar, respectively, in good agreement with experiment. © 1990 The American Physical Society.