Like any introductions, common sense and supervision are required! I've let one of my cats "sniff" my baby ball (she was in my hand...quick movements can trigger a "prey drive" in a cat so I wanted to be sure that my ball was fairly immobile). My cat took one whiff, got a very offended look on his face and walked away in disgust. As my ball gets bigger, I'll worry less as balls (especially adults) don't seem to move fast enough to interest a cat...if anything, I'd worry about the tip of the tail which is string-like and tempting...but I'd really be surprised if any problems arise! But, again, I can't stress supervision enough!