The two tiny worlds move up and down as they orbit around the planet, meaning they don't crash into each other, scientists say.
Researchers have called the behaviour a "dance of avoidance" that goes on between the moons Naiad and Thalassa.
The two moons travel around very similar orbits, just 1,150 miles apart. The dance ensures they don't ever get that close, however, since Naiad moves up and down every time it passes by Thalassa, which moves more slowly, and so they stay about 2,200 miles apart.
If you were sat on Thalassa, Naiad's movements would look like a very strange, zigzagging kind of dance. The moon would pass by twice from above, and then twice from below, repeating forever.
Those movements happen quickly. Naiad makes its way around Neptune once every seven hours, while Thalassa takes seven and a half hours.
The pattern keeps the planet's orbits stable and is like nothing ever seen before, scientists say.
"We refer to this repeating pattern as a resonance," said Marina Brozović, an expert in solar system dynamics at NASA's Jet Propulsion Laboratory in Pasadena, California, and the lead author of the new paper, which was published last week.
"There are many different types of 'dances' that planets, moons and asteroids can follow, but this one has never been seen before."
The gas giants out in the far reaches of the solar system are so huge and distant from other planets they are the dominant sources of gravity. They have each pulled in dozens of moons, each of which has its own strange back story.
Neptune has collected at least 14 moons, though scientists think there could be more waiting to be discovered. Some are very far away – such as Neso, the most distant, which takes 27 years to get around – while others are much closer.
Naiad and Thalassa are among those more intimate moons. It is thought that the two worlds found their strange resonance after the system was disrupted
"We suspect that Naiad was kicked into its tilted orbit by an earlier interaction with one of Neptune's other inner moons," Brozović said. "Only later, after its orbital tilt was established, could Naiad settle into this unusual resonance with Thalassa."
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