[en] The capture of 1s electrons into partially stripped ions has been calculated rigorously within the Oppenheimer-Brinkman-Kramers approximation taking into account both the departure from the Coulomb potential and the effect of occupied projectile states. Numerical calculations have been performed for Li/sup q/+, C/sup q/+, N/sup q/+, and O/sup q/+ colliding with H atoms. After applying a reduction factor derived from the eikonal approximation excellent agreement between theory and experiment is obtained for q = 1 and slightly decreasing agreement for q = 2. In all cases considered the partially stripped projectile behaves like a Coulomb particle with the bare charge q if q> or =3 except at very high energies. Within the present treatment it is not possible to reproduce the oscillations in the charge-state dependence of the cross section for the reaction Ta/sup q/++H→H⁺+Ta/sup( q/-1)+ observed by Kim et al