Hegemony
In the 19th century, hegemony came to denote the "Social or cultural predominance or ascendancy; predominance by one group within a society or milieu". Later, it could be used to mean "a group or regime which exerts undue influence within a society". Also, it could be used for the geopolitical and the cultural predominance of one country over others, from which was derived "hegemonism", as in the idea that the Great Powers meant to establish European hegemony over Asia and Africa.
Hegemonic stability theory
Hegemony demands power, which is defined by British scholar Susan Strange as the ability of one party to affect outcomes such that their preferences take precedence over the preferences of other parties. The question of whether the United States is still a hegemon is tied into whether or not it has lost power. 
Keohane sees power as tied into resources and production. The US GDP is now lower relative to others as there are growing economies with considerable amount of GDP such as BRIC countries. This implies a loss or decreased power of US as a hegemon.