It is normal behavior for a puppy to bother an adult dog. The puppy is looking for a playmate, and while the adult dog may or may not be willing to play with the puppy some of the time, it is unlikely he will tolerate puppy behavior constantly. Of course, if you want the puppy and adult dog to get along, you need to manage the relationship so the dog doesn't take it upon himself to put a stop to your puppy's behavior.
Provide your puppy with plenty of exercise. You can't expect your puppy to deal with excess energy in a positive way. He will try to make anyone or anything close by a playmate, and, failing that, will find some other way to get into trouble.
Place food and water dishes far enough apart that your adult dog can eat undisturbed. Resource guarding, where your dog feels like he has to protect something to keep someone else from taking it, can lead to testy behavior.
Supervise interactions between your puppy and adult dog. Eventually you hope your dogs will be the best of friends, but initially, you need to keep an eye on them when they are together. When your puppy gets too rowdy, or your dog seems like he has had enough, it is time to separate them. Don't wait until your adult dog snaps at your puppy or your puppy is so excited he is running uncontrollable circles around your adult dog.
Give your adult dog his privacy. Keep one area where the new puppy is not allowed access. If he sleeps in a crate, the room his crate is located in may make a good choice. He needs a spot he knows he can retreat to without having his head pounced on or his ears chewed. Confining your puppy to certain rooms also makes house-training easier. You will have to keep an eye on you puppy constantly to keep him out of the restricted area, but it is always a good idea to keep close tabs on your pup.
Crate your puppy if he is tormenting your dog. The crate isn't just for adult dogs. Crate training a puppy makes housebreaking much easier. You can also put him in the crate when he is feeling particularly rambunctious. This is more of a time-out than a punishment, so he can calm down and stay out of trouble.
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