Usually if you have a grown dog and bring a puppy into the home, this is usually not too much of a problem. A puppy is extremely active and will want to play with the older dog that may just get annoyed and wish it would leave him alone. The older dog may also enjoy having someone to play with and may take to the puppy as readily as you do.

Cats are a bit different. Once they get older they get set in their ways and are no longer as playful as kittens. A kitten may approach the older cat just to have the cat swat it with a paw but usually the cat will not viciously attack. It may just slink off to a place where the kitten can't get to it so that it can go back to its nap and have a peaceful place where it won't be bothered.

The important thing to do when bringing a new pet home is to slowly introduce it to the other animals. When you bring home a kitten, its going to be a bit skittish anyway, not knowing where it is and assaulted by all the new sights, sounds and smells. Its better to segregate the kitten in a carrier or a room for a while until it adjusts. This could take days so don't feel the need to rush the kitten into meeting its new older brother or sister. Whatever room you first leave it in, you will find that it is likely to spend much of the time hiding from you. It may stay under the bed until you go to sleep and it feels safe. After a while, the kitten may climb into bed with you and curl up in your hair where it most feels as it did when it cuddled up with its mother. You will know when its time to introduce the kitten to the rest of the home because it will show an interest in leaving the room by howling or scratching at the door.

Once you let the kitten out, follow it around as it explores its new home and pay particular attention if it approaches the older animals in the home. If the older animal is a dog that starts to growl, reassure the dog with soothing words. Pick up the new kitten or puppy and approach the dog with it to show that you accept the new addition. This will reassure the dog that it's ok to have it around. Let the animals sniff at each other and if the dog shows irritation then take the newer one away for a while. Don't rush trying to make them become friends.

Older cats may never actually become friends with newer ones but they can accept them and be able to live with them in a civilized manner.