Two men used forged bank notes to but items at a pub and different Co-op supermarkets in Fareham, Botley and Chandler's Ford.
Between 4.55pm and 7.20pm on November 14, two men allegedly tried to defraud three shops across the area.
The first incident was reported at The Crown Inn on West Street before further incidents at Co-op shops on Botley High Street and on Winchester Road in Chandler's Ford.
Police are looking to speak to two men in relation to the incident.
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The first is white, about 23 and has an average build and slicked-back hair.
He was wearing grey trainers, blue jeans and a grey hooded top with black writing on the left chest area.
The second man is white, in his 50s and was wearing jeans, a white shirt and grey gilet.
Police said: "We believe the men in these images can help us with our investigation and would urge them, or anyone who knows their identity, to get in touch with us."
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