In the first, a 16-year-old girl was struck on the leg as she crossed the road near to Lockerbie Academy last Wednesday at 1.25 pm.
Police Scotland sergeant Scott McDowall explained the teen had begun crossing the road when a dark grey saloon-type car drove into Dryfesdale Place from Glasgow Road direction, and hit her.
He said: “It has continued on its journey with no trace thereafter.
“So, driver and vehicle have yet to be traced and obviously we’d be keen to do so to ascertain the circumstances, etc.
“The young girl has sustained bruising and tissue damage as a result of the collision.”
Then, two days later, a second crash was reported to Police Scotland, this time involving a small white van and an elderly woman at 1.15 pm near the Flower Pot gift shop on the High Street.
Sgt McDowall said: “Unfortunately the lady suffered a fractured pelvis and was admitted to the orthopaedic ward at DGRI.
“The injuries sustained are non-life threatening, however.”
He added that the circumstances are still under review and the investigation is ongoing.
The driver, a woman, stopped at the scene and interacted with the pedestrian, along with witnesses, but left before police arrived.
Sgt McDowall added: “It was quickly established there was nothing malicious in terms of her being traced slightly later.
“She had remained at the scene with the lady and spoke with other members of the public until the arrival of help.”
Anyone with information who has yet to contact police is encouraged to do so, by calling 101, quoting incident 1594 of 17 December.