The two-center wave-packet convergent close-coupling method has been applied to model the processes of electron capture and ionisation in collisions of fully stripped neon and lithium ions with atomic hydrogen at projectile energies from 1 keV/u to 1 MeV/u. For the Ne10+ projectile, the resulting total electron-capture cross section lies between the two sets of experimental results available for system, which differ from each other significantly. For Li3+, our total electron-capture cross section agrees with the available experimental measurements by Shah et al. [J. Phys. B: At. Mol. Opt. Phys 11, L233 (1978)] and Seim et al. [J. Phys. B: At. Mol. Opt. Phys 14, 3475 (1981)], particularly at low and high energies. We also get good agreement with the existing theoretical works, particularly the atomic- and molecular-orbital close-coupling calculations. Our total ionisation cross section overestimates the experimental data by Shah et al. [J. Phys. B: At. Mol. Opt. Phys 15, 413 (1982)] at the peak, however we get good agreement with the other existing theoretical calculations at low and high energies.