You hoped they would become friends on the first day. Instead, one dog follows the other around the room, and the dog who lived here first keeps retreating. It can be tempting to stand back and let them "set boundaries." A warning growl is information, but a household should not depend on a dog having to warn again and again before you make space.
Dogs Trust recommends careful introductions, separate resting and feeding areas, supervision in the first days and separation when you cannot watch. Friendship, if it develops, takes time. Peaceful coexistence is already a good outcome.
Before they share a room
If the first meeting has not happened, plan it in a suitable neutral area with enough room for the dogs to move apart. A walk with one handler per dog can start at a distance where both are relaxed. Close the gap only if both remain comfortable. Avoid face-to-face pressure and crowded doorways. If the newcomer is a puppy, ask your vet about safe meeting locations and vaccination risks before choosing a public place.
At home, set up two resting places and separate water and food areas. Feed in different rooms or behind secure barriers. Put high-value chews and toys away during early introductions if they create competition. Neither dog has to prove they can share a bowl, a bed or your lap. Give the resident dog access to familiar quiet spaces and the newcomer their own retreat.
Keep contact brief and optional
Supervise early interactions. Let the dogs investigate for a short time, then calmly call them apart for a break. If one keeps following and the other keeps leaving, the break is not a failure. It gives the dog who wants space a chance to rest. When you cannot supervise, use separate rooms with a closed door or a reliable barrier appropriate for your dogs. Do not rely on "they were fine for an hour" as proof they are ready to be alone together.
Look for loose bodies, voluntary approaches and the ability to disengage. A stiff body, hard stare, repeated avoidance, guarding, growling or snapping calls for distance. Do not punish the growl, change the setup so neither dog has to defend space or food. Dogs Trust recommends separating them immediately if there is marked discomfort and getting professional advice before another introduction when aggression occurs.
Protect the dog who is not having fun
An older dog may find a bouncy puppy exhausting. Give the puppy appropriate play and rest elsewhere rather than asking the older dog to entertain them. Some dogs prefer little or no physical play with their housemate. That is not a problem if each dog can eat, sleep, move through the house and spend time with people without feeling pressured.
Watch for signs of pain or fatigue in either dog, especially if one has changed behavior suddenly. A vet can check a medical contributor. If a fight happens, protect people from injury while separating the dogs safely, do not reach between their mouths. Seek veterinary care for injuries, even punctures that look small, and qualified behavior help before attempting reunion.
Common mistakes
The first is making them eat side by side to "bond." Competition at a bowl can increase tension. The second is leaving them together unattended after one apparently good greeting. The third is forcing repeated nose-to-nose meetings when one dog keeps trying to leave. Avoid using a growl as proof that a dog is "bad" or as permission for the other dog to keep pestering them.
Progress may look boring: two dogs resting in separate spots while nothing happens. That is a useful first week. Tonight, put food and beds in separate areas and plan one calm, supervised interaction you can end before either dog feels trapped. For more on introductions and sharing a home, see the second-dog introduction guide, keep separate rest and feeding spaces in place meanwhile
Sources: Dogs Trust, "Introducing your new dog or puppy to your current dog": https://www.dogstrust.org.uk/dog-advice/life-with-your-dog/at-home/introducing-new-puppy.