The interaction of two molecular oscillating tori is theoretical investigated using the methods of classical molecular dynamics. In the paper, we found that a group of carbon nanotori located near each other is subject to a collective flip effect similar to the Dzhanibekov effect. The influence of intermolecular interaction and the initial conditions of dynamics on motion and a flip effect (pi-rotation) of the system of two nanotori is studied. The conditions under which the motion of molecular tori becomes unstable due to the flip effect are discussed.