5335 Damocles (// DAM-ə-kleez) is the archetype of the Damocloids, asteroids that are inactive nuclei of the Halley Family and long-period comets. It was discovered in 1991 and named after Damocles, a figure of Greek mythology.
When Damocles was discovered, in 1991 by Robert H. McNaught, it was found to be on an orbit completely different from all others known. Damocles's orbit reached from inside the aphelion of Mars to as far as Uranus. It seemed to be in transition from a near-circular outer Solar System orbit to an eccentric orbit taking it to the inner Solar System. Duncan Steel, Gerhard Hahn, Mark Bailey, and David Asher carried out projections of its long-term dynamical evolution, and found a good probability that it will become an Earth-crosser asteroid, and may spend a quarter of its life in such an orbit. Damocles has a stable orbit for tens of thousands of years before and after the present, because its highly inclined orbit does not take it near Jupiter or Saturn.
There is some speculation that 5335 Damocles may have a meteor shower associated with it on Mars from the direction of Draco.
The adjectival form is Damoclean, /dæməˈkliːən/.