Travellers have been spotted at Summerseat Park on Waterside Road in the past week.
It is thought they have been there since Saturday, 3 June and part of the wooden fence that surrounds the park has been damaged to gain access.
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Last July, travellers were spotted on the park and a padlocked gate was built at the entrance from Ruby Street.
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Around six caravans and a number of cars are currently on the site and residents have said they have heard quad bikes being driven around the area.
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North Manor Councillor Liam James Dean said: "I completely support my residents, many of whom have contacted me about this - the reports of anti-social behaviour are completely unacceptable and I hope are resolved fast.
"I have liaised with both Bury Council Officers and GMP on what steps can be taken and how we can expedite the process.
"The police now have had new powers granted to them to react to these instances and I hope they are used appropriately in this case.
"We've had this problem previously, and took measures to prevent it, it now seems the fence has been deliberately cut to gain access to our field - this is criminal damage and I hope the police will take the appropriate measures against those who did it.
"Should anyone witness anti-social behaviour please report it to the police using 101, and please raise concerns with me that I can chase up."
Bury Council have been contacted and asked if an eviction notice has been issued.
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