Thanks so much for the additional information.
An occasional gagging with food or mucous produced wouldn't concern me too much since it doesn't take much to trigger this reflex in a cat. There could be any number of possible causes such as late onset inflammatory bowel disease or rapid ingestion of food or a hairball problem.
And, since it's doesn't happen very often, then this is less reason to be terribly worried about it.
However, coughing can sometimes be a little different since this isn't something that a cat typically does. And, unfortunately, there could be a number of possible causes for it, ranging from not too terribly serious to possibly more worrisome.
1. Feline Asthma is a very common cause of coughing in a cat. This condition is similar to that seen in a human where there is inflammation in the lungs which is triggered by something in the environment such as pollens, smoke, aerosol sprays, etc.
This is often a somewhat difficult diagnosis to make. Chest x-rays might be suggestive as would bloodwork (eosinophils might be elevated but they aren't in every case). I often diagnose this condition based on a cat's response to steroids. If they are 100% better, then this is the diagnosis. It may seem like a crude way to diagnose this condition, but if I rule out other possible reasons for the signs first (see below)then I don't worry about side effects from steroids.
This LINK discusses this condition in detail.
2. Bacterial infections such as Bordetella or mycoplasma infections can also cause a cat to cough and are equally difficult to diagnose in some cases. If I suspect that this might be the cause, (especially if she's an outside cat), then I'll dispense Doxycycline 5 mg/kg twice a day to rule them out.
3. If Nelly is an outside cat, then lung worm is a possibility. This is a parasite that is most often diagnosed with a fecal sample. One effective treatment would be panacur.
4. Heartworm disease. This disease is transmitted by mosquitoes and depending on where you live, may be a possibility. We do have a test for this which is often done in a vet's office. Unfortunately, we don't have an effective treatment for it in cats. This disease is different in a cat than in a dog and the coughing is related to inflammation in the lungs.
Steroids can be used to treat this inflammation. This LINK discusses this condition.
5. Heart disease. These cats usually have other signs in addition to coughing such as weight loss or exercise intolerance. Stress might trigger a worsening of the condition. A chest x-ray can be useful in determining if there is an enlarged heart or fluid in the chest but ultrasound is usually needed to determine the exact diagnosis.
Some cats can develop esophagitis which can sound somewhat similar to coughing but isn't exactly vomiting either. If you think she might have this condition, you could safely give her over the counter Pepcid AC, 1/4th of a 10 mg tablet twice a day.
I hope this helps and gives you an idea of the many possible explanations for her behavior. I wish I could narrow the list down for you but, unfortunately, there are just too many possible reasons for her behavior.
But, should be too worried? I wouldn't be at this point because she's not otherwise acting ill. Deb