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Council parks and cemetery manager Scott MacLean said in a statement the traps had been found recently in the gully.
A council contractor was checking the area and removing traps as they were found, but dog owners were warned to be cautious, he said.
"We're also advising neighbouring residents as there may be a risk for cats if they roam in the area.''
The traps were likely to have been set by people wanting to trap possums for their fur, he said.
While possums were considered a pest, people were not allowed to set traps on council land without permission, he said.