The zeroth-order regular approximation (ZORA), a two component approximation to the Dirac equation that was earlier formulated and tested within the framework of density functional theory, is generalized to a treatment based on the Dirac-Fock equation. The performance of the ZORA equation and an improvement known as scaled ZORA is investigated, in particular with respect to orbital energies and various radial expectation values in the case of the xenon and radon atoms. The results of the simple ZORA approximation are shown to be quite close to the full Dirac-Fock method, except in the deep core region where the scaled version of the method is needed. It is found that a further approximation in which the density is calculated from the two-component ZORA orbitals alone gives satisfactory results, which is an important result from a practical point of view since in this way one can avoid calculating any two-electron integrals involving small-component basis functions. © 1995.