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.
Counterhegemony
If a counterhegemony grows large enough it is able to subsume and replace the "historic bloc" it was born in. Neo-Gramscians use the Machiavellian terms "war of position" and "war of movement" to explain how this is possible. In a war of position a counterhegemonic movement attempts, through persuasion or propaganda, to increase the number of people who share its view on the hegemonic order; in a war of movement the counterhegemonic tendencies which have grown large enough overthrow, violently or democratically, the current hegemony and establish themselves as a new historic bloc.