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
Neorealists have been focusing on this theory recently, the main proponent of it being John J. Mearsheimer who is trying to incorporate it into 'offensive realism'. In his book 'The Tragedy of Great Power Politics' Mearsheimer outlines how the anarchic system that neorealists subscribe to (see Kenneth Waltz for original theory) creates power hungry states who will each attempt to install themselves as regional and global hegemons. His theory is not widely embraced by fellow realists who argue that the hegemon supports the system so long as it is in their interests. The system is created, shaped and maintained by coercion. The hegemon would begin to undermine the institution when it is not in their interests. With the decline of a hegemon, the system descends into instability. Other realists argue that the anarchic system does not actually give causal motivation to aid the creation of hegemons.