If you already have a cat and bring home a new cat or kitten, introduce them to each other slowly. Cats are territorial, and the established cat may hiss or growl at a strange cat in his house.
Kittens are not usually territorial toward another kitten, and they may immediately run off to play together. However, if you introduce a kitten to an adult cat, the kitten may be afraid of the bigger cat until they get to know each other.
To introduce cats, place the new cat in his carrier and let the two cats see and sniff each other through the carrier door. Then place the established cat in his carrier and allow the new cat to wander around the house and sniff the other cat. You can also let the established cat sniff the new arrival cat under a door. This will allow them to get to know each other's scent and prevent any fighting.
When you feel that the two cats are ready to meet, introduce them to each other in a neutral place. Watch how they interact, and be prepared for some growling, hissing or swiping. This is natural. When the cats become familiar with each other, they will establish a hierarchy and accept one another.
As a precaution, do not leave the cats alone until you are sure they will not fight. If they seem very agitated with each other, separate them and reintroduce them again the next day,
Once the cats have learned to get along, spend time petting, grooming, or playing with each cat in turn so that one does not get jealous of the other. When a new cat is introduced into the home, the established cat may feel like he is being replaced which could lead to behavioral problems such as aggression or depression.
Reassure the established cat that he is loved. Pet him a lot, play with him often, and give him extra attention. Do not show favoritism to the new cat or kitten or ignore your other cat.