We present theoretical single to quintuple ionization cross sections for Ne, Ar, Kr and Xe bombarded by H + and He + . Post-collisional contributions due to Auger-like processes are taken into account using recent photoionization data. The present continuum distorted wave-eikonal initial state (CDW-EIS) and first Born approximation results are compared with the experimental data available in the energy range of 50-10 000 keV amu −1 for H + on Ne and Ar, and 50-1000 keV amu −1 for the other cases. In general, the combination of the CDW-EIS with the post-collisional branching ratios describes well the multiple ionization data above 300 keV amu −1 , showing a clear tendency to coalesce with the first Born approximation at high energies. The surprising result of this work is the good performance of the first Born approximation which describes rather well the experimental data of double and triple ionization, even in the intermediate energy range (50-300 keV amu −1 ), where direct ionization is the dominant contribution.