Deuteron transfer in heavy water is investigated by means of mixed quantum/classical molecular dynamics simulation and compared to proton transport in water, which was treated in a previous study [D. Zahn, J. Brickmann, Isr. J. Chem. 39 (1993) 483]. Therein the migration of a positive charge is treated as a two-step process; (i) the displacement of a H3O+/D3O+ ion, followed by (ii) proton/deuteron transfer to an adjacent (heavy) water molecule. The water molecules as well as the H3O+/D3O+ ions are treated classically. The proton/deuteron transfer between two neighbor molecules is treated on the basis of a quantum degree of freedom. It is shown that our model allows a numerically very effective simulation of proton/deuteron transfer processes in aqueous solution.