The cross section for double charge transfer between H + and H − at low collision energies (E 90 eV) is calculated using a many-state molecular close-coupling model. The wave function is expanded in a diabatic representation of the seven lowest 1 + g and the six lowest 1 + u states of the hydrogen molecule. The calculated cross section shows clear oscillations as a function of the collision energy, similar to those observed experimentally. However, the magnitude of the calculated cross section is larger than found in experiments. Also, the cross section for double charge transfer in collisions between D + and H − is calculated.