- "So... is the Galactic Alliance good or evil?"
"Eh, eh, a little from column A, a little from column B."
- ―Ben Skywalker and Natasi Daala
The Galactic Alliance, or the Galactic Federation of Free Alliances, or the Galactic People's Union of Free Federations of Democratic Coalitions of Commonwealths of Representative Alliances of Independent Republics, was a government that came into being when the Yuuzhan Vong scared the living bejesus out of everyone and made the New Republic collapse. Just call it the "Galactic Alliance" for short. Galactic Alliance = Galactic Empire + Rebel Alliance, good and evil combined into a soft-hearted, totalitarian, wishy-washy mess.
Cal Omas was the first Chief of State of the Galactic Alliance. His first act as leader was to remove all images of himself from the HoloNet archives and from the currency. The government was founded by the surviving independent systems of the New Republic as well as the relatively unscathed Imperial Remnant, led by Gilad Pellaeon. Omas demonstrated superb leadership skills... by sitting back and doing very little while Luke Skywalker and Jacen Solo kicked the Yuuzhan Vong's ass, thus winning the war.
Omas stayed in power for 12 years. Then Jacen Solo, who had developed evil-looking yellow eyes, which nobody had really noticed, deposed him and replaced him with fish-boobs. Er, that is, Cha Niathal. She had fish-boobs. Then evil Jacen revealed himself as the Sith Lord Darth Caedus and took over as the new Chief of State, replacing fish-boobs. At this point, the people of the "Galactic Alliance" were beginning to wonder, "Hey, didn't we used to have elections?"
But hey, no worries. Once Admiral Daala took over, everything was just swell, because Karen Traviss finally managed to get an entire government devoted to hating the Jedi. Years and years later, the whole thing fell apart all over again when Darth Krayt showed up... but none of that really counts as canon, does it? Nah.