my new puppy

He could just have a little puppy cold. But if it persists and his behavior changes, then I would take him to the vet and see if there is any thing really wrong.

If the dischrge from his noe is yellow or green, from one side of his nose, or has coughing along with his runny nose, take him to the vet. A runny nose is a sign of a possible upper respatory infection. You may just want to call your vet (most vets won't tell you to bring your puppy in unles they really think something is wrong).