Three elderly women had their purses or bank cards stolen while they were out shopping in Marlborough and Devizes last Thursday.
Police are appealing for information about the offenders and say the incidents could be connected.
The first occurred at Waitrose in Marlborough about 11.15am.
As the victim left the store’s lift to go to the car park, a man and a woman who spoke in a foreign language dropped some loose change on to the floor and gesticulated that the money was hers.
Despite her protests, the couple were very persuasive and she took some of the money but, after leaving the lift, she realised that her purse and two bank cards were missing.
Thieves struck again at Tesco in Devizes about 12.45pm.
As in the first incident small change was dropped on the floor next to an elderly woman after she had paid for her shopping.
A couple attempted to persuade the woman that the change was hers and assisted her in picking it up.
Afterwards the woman discovered her debit card was missing.
The third incident occurred at Lidl in Devizes between noon and 12.50.
Another elderly woman heard a crash from a nearby aisle and found staff cordoning off an area containing some broken bottles.
Upon reaching the checkout, the woman noticed that her purse was missing from her handbag.
Police say the foreign woman is described as white but dark skinned, in her mid 30s, with long dark hair, and about 5ft 7inches tall.
She was wearing an olive green dress with another skirt underneath, a thin white belt and black sandals and was carrying a black handbag.
The man in the first incident is described as of South American descent, slim, in his late 30s, with receding hair. He wore blue faded jeans and a black jacket with white stripes on the sleeves and around the bottom.
The man in the second incident is described as white but dark skinned, with black hair and in his early 20s and wearing a blue jacket.
Sgt Ian Thomas said: “These offenders targeted elderly, vulnerable people and I am keen to apprehend them as quickly as possible to prevent any further victims.
He asked anyone with information on the offenders or who was in Marlborough or Devizes that day and saw anything suspicious to contact him on 0845 408 7000.
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