Īs of August 2021 this list from the JPL SBDB contains 20 numbered and 268 unnumbered bodies that meet Akimasa Nakamura's criteria for being classified as a damocloid, that is, either a retrograde orbit, or the following orbital elements: q 8.0 AU, and e > 0.75 (also see § top).
Retrograde objects such as Halley's Comet and damocloid (343158) 2009 HC 82 can have relative velocities to Earth of 81 km/s (290,000 km/h). Damocloids are reddish in color, but not as red as many Kuiper-belt objects or centaurs.
The albedos of four damocloids have been measured, and they are among the darkest objects known in the Solar System. Their average radius is eight kilometers assuming an albedo of 0.04. Of these objects, 189 have orbital observation arcs greater than 30 days providing reasonably decent orbits. Using the Tisserand's parameter with respect to Jupiter of 2 or less, there are currently 220 damocloid candidates as of July 2021. However, this definition that does not focus on Jupiter excludes objects such as (127546) 2002 XU 93, 2003 WG 166, and 2004 DA 62. David Jewitt defines a damocloid as an object with a Jupiter Tisserand invariant (T J) of 2 or less, while Akimasa Nakamura defines this group with the following orbital elements:
Damocloids are a class of minor planets such as 5335 Damocles and 1996 PW that have Halley-type or long-period highly eccentric orbits typical of periodic comets such as Halley's Comet, but without showing a cometary coma or tail.