The migration of the primary/peritectic interface in local isothermal condition is observed in dendritic structure of Sn-Ni peritectic alloy after experiencing interrupted directional solidification. It was observed that this migration of primary Ni3Sn2/peritectic Ni3Sn4 interface towards the primary Ni3Sn2 phase was accompanied by migration of liquid film located at this interface. The migration velocity of this interface was confirmed to be much faster than that of peritectic transformation, so this migration was mostly caused by superheating of primary Ni3Sn2 phase below TP, leading to nucleation and migration of liquid film at this interface. This migration can be classified as a kind of liquid film migration (LFM), and the migration velocity at the horizontal direction has been confirmed to be much faster than that along the direction of temperature gradient. Analytical prediction has shown that the migration of liquid film could be divided into two stages depending on whether primary phase exists below TP. If the isothermal annealing time is not long enough, both the liquid film and the primary/peritectic interface migrate towards the primary phase until the superheated primary phase has all been dissolved. Then, this migration process towards higher temperature is controlled by temperature gradient zone melting (TGZM).