In the first incident, an elderly woman’s handbag containing £300 was stolen and a further £200 was taken from her bank accounts.
The woman had just withdrawn cash from Santander on High Ousegate.
She hung her bag containing the cash on her walking aid as she shopped in Marks and Spencer on Parliament Street.
Police believe it was unhooked from her walking aid and stolen by a man and woman while she was in the shop.
Thieves later used her stolen bank cards to withdraw £200 from an RBS cash point on Nessgate, York.
Further attempts to withdraw another £500 were unsuccessful after officers helped the victim alert her bank.
The second incident happened at Boots in Coney Street. An elderly woman’s purse was stolen as she shopped, again from her walking aid, by a woman who then left the store.
Both victims are in their mid-to-late 70s.
The incidents happened on 18 and 20 November respectively and an extensive investigation was launched after they were reported.
During investigations, police established that the two incidents are linked.
Further investigations then enabled officers to identify two people they want to speak to in connection with both incidents, and locate CCTV images of them.
A police spokesman said: "Officers have been working hard to gather information, including CCTV footage, and support the elderly victims.
"We'd ask members of the public who think they may know the people pictured to get in touch.
"With shops busy during the January sales, we'd also urge shoppers to remember to keep bags securely closed and keep possessions with you and in your sight at all times."
If you recognise the man and woman pictured by CCTV or have any further information that could help the investigation, please contact North Yorkshire Police on 101, select option 2 and ask for Matthew Roebuck.
You can also email PC Roebuck on [email protected] or call Crimestoppers anonymously on 0800 555 111.
Please quote reference 12170207415 when passing on information about the first incident or 12170208454 for the second.