Evidence that the population of the animals on the Isle of Arran is "fit and healthy" is good news for the future of the species, scientists say.
The UK's native red squirrels are increasingly under threat from disease and the spread of grey squirrels introduced from North America in the 19th century.
Arran is one of 19 strongholds for the species in Scotland where there are no grey squirrels.
A team of researchers trapped and examined 21 of the animals last summer, as well as looking at the remains of 16 red squirrels killed on the roads. They found no sign of squirrelpox, a virus often carried by grey squirrels, which is usually fatal to the red species.
The survey was led by vets and scientists at the University of Edinburgh's Royal (Dick) School of Veterinary Studies and funded by the People's Trust for Endangered Species and Forestry Commission Scotland.
Professor Anna Meredith, who worked on the survey, said: "Some populations of red squirrels have been found to have high levels of diseases, and lack of genetic diversity could also affect their health, so we're delighted to find that Arran's red squirrels are fit and healthy."
She added: "Arran's squirrels would be an ideal 'Arc population'. As long as we can keep them healthy and genetically diverse, if we need to repopulate areas of Scotland with red squirrels this would be an ideal source."