Symptoms of an allergic reaction include itchy and swollen eyes, sneezing, coughing and breathing difficulties - similar to those suffered when people have a cold.
The most common cat allergy comes from the Fel d 1 allergen which is passed on by cats through saliva.
When they clean themselves, the saliva, hormones and microscopic skin cells - known as dander/dandruff - pass on to their coat, and that is when the human suffers the allergy.
What happens, the scientists say, is the human body misidentifies cat dandruff as something more harmful than it is.
Allergic reactions are the result of the immune system over-reacting to a perceived danger.
Instead of identifying and responding to a harmful virus or bacteria, the immune system misidentifies different allergens, including dander, as dangerous and mounts an immune response.
That in turn triggers a huge immune system response in the human.
Now, for the first time, the scientists involved in this report suggest it will be possible to develop a drug that will control such an allergy.
It is hoped that drugs already developed to tackle other conditions could now be applied to help cat allergy sufferers.
"How cat dander causes such a severe allergic reaction in some people has long been a mystery," said Dr Clare Bryant, lead author of the research from the University of Cambridge's Department of Veterinary Medicine.
The researchers are confident that they will not only be able to find something to deal with allergy to cats, but such a drug would also benefit those who are allergic to dogs.
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