It is unlikely you will be able to avoid action between the Pets under the title “Who’s boss”. The struggle will be fought for any place in the house. Even the seat on your lap. So be prepared for the fact that, while your Pets will get along, peace in your home will not.
Remember, if you are going to get a dog and cat in the same house. If you don’t already have an animal, but you want to have both, it’s worth taking a kitten and a puppy and not an adult Pets. So it will be easier for them to get used to each other, and none of them will feel that his place in the house was taken by someone else.
And if you already have an adult cat or dog, you should not immediately tune in to the fact that he does not like the new. It is possible that your pet will treat the new pet as a kitten or a puppy: will take care of it in every possible way and play with it.