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Senior Sergeant Liz Waru said police have a warrant to arrest Phillip Jamie Stretch (31) and Ondray Ngatauemaha Marsh (35).
Mr Stretch was described as medium build, 189cm, with multiple tattoos, including a leaf and tribal band on his right forearm and the words `EAST SIDE' on his upper right arm.
He was considered unpredictable and should not be approached, Snr Sgt Waru said.
The men could be anywhere in the Dunedin area but particularly around the town belt.
Anyone with information is urged to call the Dunedin Police Station on 471-4800.
Police could not disclose the offences the men were being sought for.