The Hartree-Fock equations are derived and generalized to the case of nuclear matter using the Brueckner reaction matrix. The Fourier transform of the nonlocal term in the resulting integral-differential equation is expanded to second-order terms, and the equation is reduced to a differential equation. An iterative method is used to obtain a self-consistent solution. Several expansion procedures were tried, and in all cases the iterations converged to reasonable values for potentials, wave functions, and binding energies for 016.