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The council said the marmosets are native to Central and South America and would be likely to seek out a warm place to spend the night.
"Check bird boxes, garages and sheds," the city council said on its website. "Please do not attempt to catch the monkeys as this may cause risk of injury to yourself or the monkeys and please do not try to feed them either."
Local police said they are aware of the escaped monkeys and the investigation has been turned over to the RSPCA.