A team of asthma and allergy experts from America looked at over 200 children's immune response to cat and mite allergens.
Just under 50 of the children had some asthma symptoms
They found that some children developed a tolerance, protecting them against cat allergies, because of a particular type of antibody they developed.
The research, published in The Lancet, found some children who had been exposed to cat allergens can develop an immunity to asthma.
But the finding does not apply to everyone.
'Immunity'
Professor Thomas Platts-Mills, who led the research carried out at the University of Virginia Asthma and Allergic Disease Center, told BBC News Online that children were just as likely to have immunity to cats as to be allergic to them.
And he said this particular type of immunity developed when children had a significant amount of exposure to cats.
"If the child goes away to college and has less exposure, they may become allergic again.
"We think children are more likely to become allergic if everyone else has got cats and they have not."
He said children who were allergic to cats are more likely to develop asthma, while those who had this particular immune response were not.
"If you're talking to parents who are going to have a child, you would not say they should give the cat away, because this response is as common as allergy."
Families 'may keep cat'
The researchers said their findings do not support the common perception that families should avoid having a cat to prevent their children developing asthma.
They wrote: "In our data, high exposure appears to be protective of some children and a risk factor for others, and it is possible that this difference is genetically controlled."
Dr Mark Larche, senior research fellow for the National Asthma Campaign, said: "The findings are very interesting and do indicate that in some cases exposure to high levels of cat allergens does induce a protective response.
He added: "This fits with what we know about successful immunotherapy, in that protective or "blocking" antibodies have been found in patients who have benefited from this form of treatment."
But he warned: "Caution should be exercised, however, as the findings may be peculiar to cat allergens and the individual."
A spokesperson for the Cats Protection League welcomed the research, and said: "Many people give up their cats or feel they can't have a cat because of their asthma or their children's asthma."
She said people mistakenly thought that by removing the cat from the home, seen as the obvious factor for asthma, they will eliminate the problem.