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.
Posthegemony
The predictions of these individuals represent the fluidity of power over time, through the idea that, during the period where the US was unequivocally dominant, people could still see the inevitable future, of a change in power and authority, on the world stage.