Accurate calculations of the near resonant charge exchange crosssections in HD+, HT+ and Dr at very low energies are presented. The charge exchange process between an ion and its parent atom is a near resonant process that becomes inelastic when two different isotopes are involved. We find that, at very low energies, the charge exchange cross-section follows Wigner's law for inelastic processes and becomes much larger than the cross-section for elastic collisions which tends to a finite limit. The efficiency of inelastic charge exchange increases as the mass difference between the two isotopes decreases. © IOP Publishing Ltd and Deutsche Physikalische Gesellscha.