<p>Oscillations in the cross sections for single-electron charge-exchange of fast nonrelativistic positive ions on a hydrogen molecule are considered. The charge-exchange cross sections for the protons and alpha particles at fixed orientations of the hydrogen molecule are calculated as functions of the energy of the incident particles using the representation of the impact parameter in the Brinkman–Kramers approximation with normalized capture probabilities. The cross sections averaged over all orientations of the molecule are also presented. The results are compared with the available experimental data.</p>