Coughing In Feral Cats
The reasons for coughing in feral cats is going to be the same as for domestic cats only the feral is obviously more exposed to viral and bacterial infections and serious ill health so you are more likely to see a feral cat coughing than a well cared for domestic cat.
As it happens, I have a page on the website about the cat cough, which may help concerned people to diagnose a possible cause...Cat Cough.
That said the only way to deal with a feral cat that has a cough that looks like something serious (and not all coughs are serious) is to trap the cat and take him or her to a vet and there are very few people who are prepared or who have the equipment and know how to do that.
Most coughs that require no action are due to foreign objects in the throat and which can be removed by coughing.
All the other causes will require veterinary treatment. If a cough lasts more than 5 days it requires veterinary treatment1.
1. Cat Owner's Home Veterinary Handbook - Drs Carlson and Giffin
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