...so, let's take a look at those two appearances!
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Green Arrow and Speedy have some problems with three super powers criminals in Star City who steal a meteor. Thinking they might be aliens, Green Arrow calls in his JLA teammate, the Martian Manhunter, for help, but the three beat the bowmen again, as their leader, Vulkor, defeats J'onn J'onzz. J'onn uses Dr. Erdel's machine to go back to Mars to learn about the villains as Green Arrow and Speedy face them again, this time with the villains capturing Green Arrow, with a mental compulsion placed in his mind to work against the Martian Manhunter. As planned, Green Arrow works against the Martian Manhunter when next they meet, but J'onn disguises himself as Green Arrow, which allows him to get close enough to Vulkor to defeat him, while knowing their enemies are Martians, allows Green Arrow and Speedy to use their knowledge of J'onn, and Martian's weakness to flame, to stop the criminals. Then, the Martian Manhunter takes them back to Mars for imprisonment.
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Flash and the Martian Manhunter are attending a fair with an exhibit on the Justice League, when they have to face an alien mutant android that manifests the powers of the Justice League members two at a time. Even worse, the alien turned its rocket into a bomb, that was going to explode, and destroy the Earth. J'onn flies to Argon, the home of the creature, to learn of its history, and that the planet was ruled by Tatania. To attempt to fool the creature into leaving Earth, J'onn calls on Hawkgirl (who's husband, Hawkman, just joined the JLA) to disguise herself as Tatania, to convince the menace to leave Earth. Only problem is the creature sees through the disguise, and almost detonates the bomb, before the real queen arrives, wherein the android destroys himself on command, saving Earth from the bomb.
Green Arrow would return time and time again to team-up with Batman (being his partner in B&B most often; though Flash tried to give Green Arrow a run for his money). Flash had the uniqueness of being the second most used host of B&B after Batman....but, sadly, the Martian Manhunter never returned to meet Batman in B&B, though J'onn did meet with Superman solo, once in World's Finest Comics, and once in DC Comics Presents.