It is not clear from Picard's remark in "Up The Long Ladder" that the European Hegemony was an actual political organization or what relation it may have had with the actual European Union or the later European Alliance. Recognizing this as mere speculation, I offer the following possible insight.
Hegemony is the leadership or predominant influence exercised by one nation or group of nations over others, and may or may not imply interest in dominance in global affairs. The surviving European Union may have assumed a hegemonic role the post-WWIII Earth (presuming the United States being unable to) and directed global reconstruction efforts. It could have become an actual intergovernmental alliance, or been simply the recognized global order in place at the time. The latter more accurately reflects the term "hegemony" and is consistent with Picard's reference to it as "the first stirrings of world government on Earth." Tfleming 02:45, 14 October 2006 (UTC)
removed stuff Edit
These two paragraphs were recently removed from the bg section by Pseudohuman. As I understand it's it's generally good practice to archive removed notes on the talk page, which hasn't been done, and since they were so extensive I've taken it upon myself to put them here myself: -- Capricorn 14:25, June 12, 2011 (UTC)
It remains unknown which competences this alliance carried, since Earth was governed by the United Earth Government since the 22nd century. However, the European Alliance might have begun as a joint effort of the European people to create a unified administration and representation at the global government and, thus, might have been very similar to the European Union.