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The story of JLA/Avengers begins when Krona, the Maltusian who caused the original DC Universe to split into infinite realities, travels to the Marvel Universe seeking the truth of creation. There he meets The Grandmaster, who proposes they test their respective Universes against one another. Should Krona win, The Grandmaster offers to guide him to Galactus, the only being in the Marvel Universe to have witnessed the creation of existence . Should Krona's Universe lose, he is to spare the Marvel Universe from entropic destruction. Krona accepts, and the battle begins, pitting the Justice League of America (chosen to represent Grandmaster) and Avengers (representing Krona) against one another.
It is not long before the JLA and Avengers encounter one another, with the former prompted by The Grandmaster to search for twelve artifacts of power in order to save a universe, and the latter instructed by Metron of the New Gods to stop the League to prevent their world being destroyed. The hunt for the items of power begins, as various Leaguers and Avengers travel across the two universes and fight each other to retrieve the artefacts In the end, both teams meet in the Savage Land and engage in an all-out battle royale for the Cosmic Cube, which is seized by Batman, earning the JLA victory. Krona, choosing not to fulfil his end of the bargain, summons Galactus and attempts to force the knowledge he seeks out of the World-Devourer. Galactus is saved by The Grandmaster, who uses his remaining strength to merge the two universes together into a single reality.
Though seemingly stable, this new reality begins to slowly fall apart due to the original universes' incompatibility. This prompts the JLA and Avengers to join forces and avert the crisis. They are taken to a dying Grandmaster by the Phantom Stranger, and informed that Krona is trying to destroy this new reality by further merging the original two universes.
The heroes storm Krona's base, fighting numerous Marvel and DC villains in the process. The battle is eventually joined by every single hero to have ever been a member of the JLA and Avengers, allowing them to defeat Krona and restore the universe to their original singularity.
NOTE: Indicia titles issues #1&3 as "JLA/Avengers" and issues #2&4 as "Avengers/JLA".