It is easy to mistake coughing for an attempt to vomit or bring up a hairball. When coughing, a cat often stretches its neck forward and makes repeated thrusts with its chest without anything coming up. Asthma and other inflammatory diseases of the lower airways are important causes, but infection and other lung problems can also occur.
If you can, film an episode without stressing your cat. It can help the vet tell coughing apart from other episodes. The examination may include listening to the lungs and X-rays of the chest, and further tests are sometimes needed to work out what type of airway disease it is.
Contact a vet if your cat coughs repeatedly, starts wheezing or becomes less active. Breathing with the mouth open, obvious use of the belly to breathe, or a cat that cannot settle because of its breathing should be assessed as an emergency.