I have asthma and cats induce it. It took a while (and two emergency room visits) but I haven't had a problem now for three or four years. I have even weaned myself off the daily use of antihistamines -- although I still need them at times.

I wash my hands alot, never touch my face -- especially my eyes or nose -- after petting a cat. I avoid having the cats too near my face. Lying prone also makes it harder to breathe. Long haired cats cause me more problems than short hair.

It can be done!