  The merging of immiscible drops differs significantly from the merging of
miscible drops due to the formation of a liquid-liquid interface between drops.
The immiscibility requires the formation of a four-phase contact point, where
the drops, the gas and the substrate meet. We show that this point has its own
unique dynamics, never studied beforehand. For very different scenarios, the
propagation distance of this point follows scales with time like t^{0.5}. A
model balancing the driving and dissipative forces agrees with our experiments.
