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Detective Sergeant Stu Harvey, of Invercargill, said the thefts and burglaries took place between May 15 and this week, with the pair starting in Cromwell, moving on to Oamaru, then Dunedin and most recently reaching Invercargill.
The pair, posing as visitors, targeted cash and electronic items, including iPads and laptop computers, after earlier ''scoping'' the rest-homes. The total value of cash and items stolen was believed to be about $10,000.
Det Sgt Harvey described the offending as ''brazen'' and said it was concerning they were stealing from organisations which helped others.
''They are targeting organisations which care for vulnerable people.''
One of the men - described as being Maori, aged about 20, with a clean and tidy appearance - wore crutches and a ''moon boot'' on his left leg, but it was unknown whether he had a genuine injury.
''There do not seem to be too many problems with mobility.''
The other man was described as being Maori, aged about 18, with short black hair.
Rest-homes targeted were Osborne House and Fulton Home in Dunedin, Iona Home in Oamaru, Dunstan Hospital in Clyde, Ripponburn Hospital and Home in Cromwell and Cargill Rest Home and Rowena Jackson Rest Home in Invercargill.
It was possible other burglaries had occurred but had gone unreported.
''These are the ones that know.''
One of the incidents involved a theft from a resident, but the others involved rest-home property.
Police previously said the pair took $823 in cash, two iPads and a laptop computer from Ripponburn Hospital and Home in Cromwell.
Police had contacted rest-homes in the region and warned them to be vigilant, but the focus was now on finding out who the pair were.
Anyone with information on the two offenders was asked to contact their local police station or anonymously contact Crimestoppers on 0800 555-111.