The Xαβ exchange approximation is applied to atoms and its universal (Z-independent) character is demonstrated. Its practical applicability to molecules and solids is critically analysed by a comparison with the Xα- and HF approximations. The influence of the modifying function which is needed to make the exchange inhomogeneity correction (β-term) finite for large r is studied. The validity of the virial theorem is discussed. © 1975.