The mostly hairless tail is able to curl around the branches of trees as the possum forages for food, its grasp is aided by rasp-ilke scales and is strong enough to hold its own weight.

[2] The holotype was reported to have been collected in the Kimberley region at Violet Valley Station, and forwarded to Walter Kingsmill who presented the specimen to the Perth Zoological Gardens.

Alexander assigned the species to a new genus of the phalangerid family, Wyulda, deriving the name from an indigenous word used by the people at Lyons River for the local and common possum; the pronunciation provided by the author is "weeoolda".

Another rock inhabiting possum found in the region, the ringtail species Petropseudes dahli, has fur covering half the tail, patches of white near the ears, and a steep forehead and pointed muzzle when observed in profile.

They demonstrate great agility when climbing, assisted by a prehensile tail that is strong enough to support themselves from a branch while reaching for leaves and other food.

The maternal rearing period of the young includes 150 to 200 days within the pouch and another eight months to become independent of the mother; reproductive maturity for the female is reached after two years.

[10] They are associated with denser vegetation over rocks and boulders that provide daytime shelter and refuge, often thickets of vines rather than the closed mangrove and open woodlands favoured by Trichosurus arnhemensis.

The specimen obtained in 1917 was the only record of the possum in east Kimberley region until 2010, when they were found occurring at Emma Gorge in the Cockburn Range.

[11] Wyulda squamicaudata has disappeared at some locations, where they are assumed to have succumbed to frequent and higher intensity fires and predation by feral cats.