If this is your cat (or the cat), take her to a veterinarian to detect signs of urolithiasis. Such diseases are particularly common in neutered cats.
Please note, does not live nearby cute kitty, protecting the ownership of which, the cats take turns marking the corners in the stairwell.
If it is the cat (or the cat) neighbors, talk to them in order to take appropriate joint measures to eliminate unpleasant odors in the stairwell. Unfortunately, not always with the owners of cats can be arranged amicably, so you may have to deal with the problem yourself.
If cats, povadivshijsja shit in your entryway, you are not the owner, install intercom and video surveillance. It also happens that the owner of a cat you can't admit that his favorite is not averse to empty your bowel or bladder on the rug the neighbors. In this case, show the neighbor the video and threatened with a fine.
In that case, if the cats do not have owners, and even the intercom for them - not a hindrance in order to gain entry, carefully remove in the entrance, good fluff all the favorite animals angles with acetic acid. As repellent odors to use and essential oil and even turpentine. Can sometimes help and a special veterinary spray "Antigadin". But remember: this procedure must be repeated several times before cat finally learn the rules of behavior in the stairwell.
In any case, do not use in order to scare away cats pepper or means for cleaning materials that contain ammonia. Pepper can kill once and for all health of cats. Yes, and dog owners would be certainly against the measures, which is not the best way affects the smell of their Pets. As for means with ammonia, that smell, on the contrary, quite like cats and pushes them to commit "dirty deeds" at the entrance.