Predominatley a term of the Cold War (1945 - 1990) between the communist east led by the USSR and the capitalist west led by the US. Both of the battling nations were superpowers and the battle in the arms race of the early cold war and the conflicts of the cold war were to stop the bipolar nature of the cold war and to become the supreme world superpower. Hegemony - a military term meaning the supreme and utmost power. Both the US and the USSR were battling for hegemony during the cold war.