It is normal for cats to cough occasionally, as long as the cat has been in good health and the cough does not produce phlegm or sputum. Coughing is mostly a symptom of inflammation in the lower respiratory tract or bronchitis. Allergies can also cause coughing in cats.
Should the coughing persist, please bring your cat to the veterinarian for a diagnosis and a treatment plan. While coughing is a symptom for many common ailments, bring it to seek treatment if your cat appears ill or has experienced weight loss.
Antibiotics would be administered to your cat to treat the cough symptoms but do not stop even when your cat appears to be getting better. It is recommended to follow the course your veterinarian has prescribed to your cat.