Leapfrogging motion of vortex rings sharing the same axis of symmetry was first predicted by Helmholtz in his famous work on the Euler equation for

incompressible fluids. Its justification in that framework remains an open question to date. In this paper, we rigorously derive the corresponding

leapfrogging motion for the axially symmetric three- dimensional Gross-Pitaevskii equation. This is joint work with Didier Smets.