The first incident involved contact between a 33-year-old pedestrian from Kirkcolm and a dark-coloured motor car on Harbour Street at about 2.10 pm.
While the pedestrian was not inured, the female driver of the car drove off after briefly stopping at the scene.
She is described as being about 5′ 5″ tall, of slim build, in her 30s, with shoulder length blonde hair. The passenger was also female, again about 5′ 5″ tall, medium build, with long dark hair and dressed in black.
The woman pedestrian in this incident was accompanied by her daughter who assisted her after the collision.
Constable David Hanlon of Police Scotland at Stranraer said: “We are keen to speak to the driver of this vehicle and to any witnesses who may have seen this collision.”
In another incident, which took place at about 2.15 pm, a grey coloured Vauxhall Insignia car which was parked and stationary outside Tesco in Charlotte Street was struck from behind by a green/blue coloured car only described as an old style Vauxhall Cavalier.
Constable Scott Costly of Police Scotland at Stranraer said: “For some unknown reason the driver of this mystery car did not stop after the crash.
“I am appealing to anyone who may have been in this area and saw this crash to get in touch if they can assist us in identifying this vehicle and driver.”
Police also want to trace the driver of a silver-coloured car, thought to be a Vauxhall make, which was responsible for damaging a drystane dyke on the A712 near to Hollins, Balmaclellan.
Constable Greg Hawker of Police Scotland at Castle Douglas said: “At this point the driver has failed to report this crash and we are appealing for witnesses who may have information regarding his identity.
“It is though that the vehicle was pulled from the ditch at the side of the road by a tractor, and again appeal to the driver of that vehicle to come forward if he or she can help.”
Police can be contacted on the non-emergency 101 number.