A prototype phase diagram for the< 1 1 2 0> family of the ordered superstructures in fcc lattices is calculated in the tetrahedron-octahedron approximation of the cluster variation method. The tetrahedron-octahedron cluster combination allows for first-and second-neighbor interactions, both essential for the< 1 1 2 0> superstructures to be ground states. Calculations are carried out for positive (antiferromagnetic) nearest-neighbor pair interactions and for a ratio of second-to first-neighbor interaction energies of 0.25. Salient features of the resulting phase diagram are tricritical points in the fcc to A 2 B 2 and the fcc to A 3 B transitions, and the presence of a bicritical point at the junction of the A 2 B 2 and A 3 B critical lines with the A 2 B 2 to A 3 B first-order transition line. The A 2 B phase of the< 1 1 2 0> family is found to be stable at relatively low temperatures and in a very narrow composition range. Stability of the disordered state is investigated in k space and the< 1 1 2 0> ordering spinodal is determined.