This article discusses the prospect of the transition of the Chinese-American rivalry into an open, all out war. The problem arises from the experience of history – two leading powers eventually refer to war in order to assume their, one of them, strategic and political primacy within the relevant international order of their time. The present situation – after a demise of the international liberal order – of confrontation between the US and China is being compared to the so-called Thucidydes’s trap, which is the reference to the Peloponnesian war. The author is challenging both the comparison and the inevitability of the war between the Big Two, without however totally excluding the possibility of some military demonstrations of their resolve to push for or to defend their global status. Reasons for such an assessment are based upon negative (nuclear capabilities) and positive (economy, development) interdependence factors between the only two superpowers and the nature of the contemporary international environment, complex and tight, which will be preventing the Big Two from sliding into the world war,disastrous for all.