The evolution of internation relationships is studied by means of a mathematical model based on a popular rule of triadic interaction: “the friend of my friend is my friend, the friend of my enemy is my enemy, the enemy of my enemy is my friend, the enemy of my friend is my enemy”. The rule is shown to lead to the formation and preservation of unipolar and bipolar configurations of nations, with the strengths of relationships, both friendly and conflictual, intensifying through time. These results confirm speculations originally made in static, graph theoretic studies of the balancing of relationships within individuals, small groups and systems of nations.