Grey Squirrels and Palm Squirrels were both introduced to Australia; the Grey Squirrels have died out, and there is one colony of Palm Squirrels left in the wild around Perth Zoo, with another in captivity at Melbourne Zoo.
http://www.australiangeographic.com.au/blogs/creatura-blog/2014/10/giant-black-squirrels-one-of-the-longest-animals
"Squirrels, family Sciuridae are represented in Australia by two introduced species, the American Grey Squirrel (Sciurus carolinensis) Gmelin 1788 and the Northern Palm Squirrel (Funambulus pennantii) Wroughton 1905.
Sciurids are distinguished from the only other family of Rodentia in Australia, the Muridae, by their external form, in particular a tail bushy to the base, and by
skull differences, notably the presence of premolar teeth and a pronounced supra-orbital spine (Watts & Aslin 1981).
Both species were privately introduced to Australia in the 19th Century; Grey Squirrels to Melbourne, Victoria, about 1880 (Seebeck 1984) and Palm Squirrels to Perth, Western Australia about 1898 (Jenkins 1977). Subsequently, Grey Squirrels were introduced to Ballarat, Victoria, in 1937 and Palm Squirrels to Taronga Zoo, Sydney, New South Wales, perhaps during the 1920s.
The Grey Squirrel is now apparently extinct in Australia (Seebeck 1984). Palm Squirrels are extinct in Sydney, but a flourishing feral colony based on Perth Zoo still exists. A captive colony has been established (1979) at Melbourne Zoo, Victoria. A similar colony at Adelaide Zoo has died out.