A variational method for the self-consistent solution of the nuclear many body problem with the inclusion of correlations is formulated. The trial function in this multiconfiguration-Hartree-Fock (MCHF) theory is a linear combination of unrestricted Slater determinants. The MCHF equations are given and a simple procedure for solving them is outlined. A great advantage of this method is that it also yields the excited states. It is shown that the trial function is stable against particle-hole excitations. Therefore the Slater determinants differ from each other at least by two particle — two hole excitations. This method is applied to the Lipkin model. In the MCHF method the difference to the exact solution is reduced by a factor three to ten compared with the corresponding value in the HF approach.Instituto de Física La Plata