Abstract The application of the Brueckner theory to the nuclear many-body problem can be greatly simplified if one separates the two-nucleon interaction (for any given state and relative momentum) into a short range part vs and a long range part vl. The cut is made such that vs alone gives no phase shift for free particle scattering. If the separation is made in this way, then the presence of nuclear matter, as manifested by the Pauli principle, has only a small effect on the two-particle wave function at short distances. On the other hand, the Pauli principle drastically reduces the induced correlations due to vl. In fact, vl is the first approximation to the effective interaction in nuclear matter. This procedure permits one to systematically expand the effective interaction in terms of ts, the reaction operator for free particles caused by vs alone. The contribution of all first- and second-order terms to the binding energy of extended nuclear matter has been calculated numerically. Most of the work was done using a central spin-independent two-body interaction containing a hard core of radius 0.4 fermi followed by an attractive exponential well with parameters chosen to give infinite scattering length and intrinsic range 2.5 fermis. If the potential is assumed to act only in S-states, we obtain a minimum energy of −12 Mev per particle at a density corresponding to a nuclear radius 1.0 A 1 3 fermis. The largest of the second-order terms contributes only 5.4 Mev to the energy per particle at this density (as compared to −42 Mev for the first-order term) and the other second-order terms much less. Thus our expansion appears to converge fairly rapidly. The effect of changes in the well parameters has been investigated. Also, our method was applied to interactions used by Gomes et al., Brueckner and Gammel, and Tagami, and our results compared with some of those obtained by the above authors.