When the JLA battles two separate unstoppable menaces, Shaggy Man and a rock-creature, The Flash hits on the idea of setting them on each other; When the Shaggy Man destroys the rock creature, the JLA pits the Shaggy Man against a duplicate of himself.
An airplane, carrying mail to the Justice League of America, crashes. Two years later, the lost mail is finally delivered to the Justice League of America. Though the cases are cold, the Justice League of America decide to investigate them anyway. The Flash meets with Professor Andrew Zagarian, on a remote island. Two years ago, Zagarian accidentally brought to life a rampaging creature, that he called "The Shaggy Man", composed of a new material, called "Plastalloy". The Shaggy Man, attracted to motion, destroyed Zagarian's laboratory. Zagarian sent a message of distress to the Justice League of America.
Finally giving up on the Justice League of America, Zagarian went after the Shaggy Man himself. Zagarian set a trap for the Shaggy Man. The Shaggy Man was lured into a cavern, where vats of molten iron were poured over the creature, completely encasing it. Powerful electromagnets paralyzed the iron-infused monstrosity. Zagarian then sealed the Shaggy Man inside the cavern. The Flash's super-speed vibrations inadvertently release the Shaggy Man from it's tomb. The Green Arrow fires a stun arrow at the Shaggy Man, to no effect. The Green Arrow then blows the Shaggy Man to pieces, with an explosive-tipped arrow.
The Shaggy Man regenerates it's entire body, and resumes it's attack. The Flash lures the Shaggy Man back into Zagarian's trap, only to learn that the Shaggy Man is adaptive, and cannot be trapped the same way twice. The Hawkman attacks the Shaggy Man, to draw the creature away from the Flash. While the Hawkman is able to keep the Shaggy Man occupied, the Justice League of America is at a loss to determine a way to defeat the Shaggy Man. The other half of the Justice League of America travels to Chile, to search for a missing astronomer, Abner Michaels. The Justice League of America find Michaels being held prisoner by a giant, tentacled monstrosity.
Michaels reveals that the creature once orbited the Earth, as a second moon. Drawn down to the surface by Earth's gravity, the creature broke apart, landing across South America. Michaels had gathered many of it's pieces together, not realizing that the meteors were part of a larger, sentient horror. Soon, the alien monster was large enough to telekinetically draw all of it's disparate parts together. The terrifying creature then began feeding on the very elements that make up the Earth itself. The Justice League of America battle the tentacled nightmare, but prove unable to actually defeat it. The Flash fashions an indestructible mirror, then leads the Shaggy Man to it.
Seeing it's reflection, the Shaggy Man immediately begins attacking it. The Flash returns to the Secret Sanctuary, and learns of the search for the missing astronomer. Traveling to Chile, the Flash finds his teammates in defeat. The Flash shatters the mirror, removing the Shaggy Man's "adversary". The Flash lures the Shaggy Man to the Arrowplane, then remote flies the Shaggy Man to Chile. Upon seeing the writhing tentacles of the giant "lunar" creature, the Shaggy Man attacks. The Justice League of America observe the Shaggy Man's epic battle against Michaels' "lost moon". The Hawkman and the Green Arrow arrive with a second, unactivated Shaggy Man.
The Flash and Wonder Woman dig an enormous, and very deep, pit. The Shaggy Man shatters the "lunar" creature back into meteor fragments. The Atom guides the alien's core into the pit, making sure the Shaggy Man follows. After the Flash and Wonder Woman exit the pit, the second Shaggy Man is dropped in, and activated. The two Shaggy Men begin fighting. As the alien creature regenerates, the Shaggy Men turn away from each other, to attack it again. As soon as the creature is reduced to fragments, the Shaggy Men resume their combat with each other. The Justice League of America seal the pit, leaving the Shaggy Men, and the "lost moon", locked in combat for eternity.