Doctor Strangefate brought the original Judgment League Avengers roster together to stop an undisclosed enemy (presumably the Skulk). The original team consisted of Strangefate, Canary, Angelhawk, Iron Lantern, and the Aqua Mariner. These events occured during JLA #1. The five members didn't stay together for long, as Doctor Strangefate left the team before JLA #4.
As the series moved on, the JLA's roster expanded. in JLA #2, Goliath and Myx joined the team, though Myx only stayed until the end of the issue, leaving after realizing his intolerance of superheroes. Somewhere between JLA #2 and JLA #4, Captain Marvel also joined the team, and Iron Lantern may have left the team during that period of time. In JLA #4, the team discovered and thawed out the frozen body of Super-Soldier, who promptly joined the JLA.
In the miniseries JLA: The New Blood, Apollo, Firebird, Mercury, Runaway, Wraith, and Nightcreeper were all metamutants, who became the newest members of the JLA. The metamutants and non-metamutants eventually discovered that their views on certain things varied, and their relationships were tested when Will Magnus framed the Mariner, who was also a metamutant, for the destruction of a number of Roxxon oil tankers. The Mariner goes on the run, and when S.H.I.E.L.D. failed to capture him, the JLA was asked to capture him. They succeeded, and this was the last straw for the New Blood members of the JLA.
With the assistance of the mysterious Mister X, the New Blood freed the Mariner from where he was being held. Taking the name of JLX, the New Blood members and the Mariner fought an epic battle against the current members of the Judgment League Avengers, which at the time consisted of Super-Soldier, Dark Claw, Captain Marvel, Angelhawk, Goliath, Canary, and Hawkeye. The battle was stopped when Angelhawk faked an injury, as Angelhawk himself was secretly a metamutant. Angelhawk later ended up joining the JLX during its first series, JLX.