Two shoppers had their purses stolen this week, prompting calls for more vigilance.
On Tuesday morning, a woman shopping in the town centre had her purse, which contained a substantial amount of cash, taken.
And in a second theft, another woman also had her purse containing a credit card stolen.
Both incidents happened sometime between 10-11 am and attempts were made to use the credit cards shortly after the thefts.
PC David Steele said: “People shopping at this time of year need to be alert to the fact that there are those who come into the town to target shoppers with a view to stealing from them. On these two occasions it appears that the ladies were targeted and then their purses stolen.
“We want to hear from anyone who was in the town centre yesterday morning and ask them to think over their movements and ask themselves ‘did I see anything suspicious?’ or ‘did I see anyone who might have been acting a bit shifty in or around the town?’.”
He also revealed that offices have received reports of two men described as being Eastern Europeans seen acting suspiciously in the town on Tuesday and is keen to hear from anyone who may have come across them.
PC Steele added: “Anyone who can help should give us a call in Dumfries on the 101 number. We started our festive safety campaign to target retail crime as we move towards Christmas on Monday and are working with shop staff in an effort to cut this type of crime down.”