A small terrier dog was attacked in Carrick Road just after 9 am and later a Labrador pup was their victim in Waverley Road.
Police say the three offending animals were Staffordshire bull terrier types and appeared to be roaming free.
A spokesman said: “We want to hear from anyone who saw these incidents or who can help us identify the owners of the dogs.”
Call can be made to officers at Dumfries on 101.