In recent experiments, it was observed that the tip vortices shed from a two-bladed rotor can interact significantly. The interaction consists of a turn of the tip-vortex from one blade rolling around a turn of the tip-vortex from the other blade. Visualized in a planar light sheet, the two vortices spiral around each other prior to merging into a single vortex. One complete cycle of the oll-up process takes about one and a half rotor cycles. The wake does not contract monotonically but expands as one of the vortices moves radially outward due to the roll-up. This behavior is illustrated by the numerical calculation of the motion of a pair of ring vortices. It is observed that the pair of rings, placed initially parallel and of the same strength roll around each other, by alternate contraction and expansion of the ring radius. Numerical calculations show that the ring interaction is complicated when the rings are initially inclined. Next the case of a two-bladed rotor is considered. A lifting-line theory is used to model each rotor blade and a fully unsteady computation of the motion of the tip-vortices is carried out using a highly accurate Adams-Moulton method to advance the vortices. The modified Biot-Savart law is used to describe the vortex structure. It is shown that the tip-vortex interaction is periodic and deterministic.