A struggle for supremacy, as in There's a constant political tug of war between those who favor giving more power to the states and those who want a strong federal government. Although there is an athletic contest also so named, in which participants holding either end of a rope try to pull each other across a dividing line, the present usage, first recorded in 1677, predates it by about two centuries. The noun tug itself means “a strenuous contest between two sides,” and war refers to fighting, either physical or figurative.