[en] Inelastic excitation cross sections are calculated for the lithium-like ions N⁴⁺ and Ne⁷⁺ in several approximations. For N⁴⁺ the 1s²2s-1s²2p cross section is calculated in a 2 state close coupling expansion with exchange at 1, 2 and 4 Rydbergs (Ry). Further calculations are made for the 1s²2s-1s²2p, 1s²2s-1s²3s, 1s²2s-1s²3p, 1s²2s-1s²3d and 1s²2p-1s²3s, 1s²2p-1s²3p, 1s²2p-1s²3d cross sections at 6, 8 and 16 Ry. in a 5 state close coupling approximation with exchange and the unitarized Coulomb--Born approximation. At 8 Ry. the inelastic cross sections are calculated also in a 5 state and 8 state non-exchange close coupling approximation. To test coupling effects the 1s²2p-3s, 3p, 3d cross sections are obtained at 8 Ry. in a 2 state close coupling approximation including exchange. For Ne⁷⁺, the cross sections are calculated in the 5 state close coupling with exchange and the unitarized Coulomb--Born approximations at 14, 18 and 30 Ry. The 1s²2s-1s²2p cross section is further calculated in a 2 state close coupling approximation with exchange at 1.6, 3.2 and 8 Ry. Results for N⁴⁺ and Ne⁷⁺ show that previous calculations that neglected exchange and/or coupling are substantially different from the more elaborate 5 state close coupling with exchange results in many instances. Finally, the rate coefficients calculated from the 5 state close coupling are compared with exchange results with experimental values. In all but one instance the experimental and theoretical values agree within the limits of the experiment