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Anyone suspected of anti-social activity can be moved away from the Faversham Recreation Ground until 5pm on Sunday.
Police are reacting to complaints that the park has been plagued by vandals and teenage gangs.
Sgt Tim Hill, of the community safety unit, said: "A dispersal order has been put in place following a number of concerns of anti-social behaviour in the area.
"Local policing officers have been targeting their patrols at the recreation ground to deter nuisance behaviour.
"Early reports suggest that the minority of people who were causing anti-social behaviour have stayed away from the area without formal police intervention.
"I have personally been to the park and spoken with a number of young people who have been extremely well behaved and were a credit to their families and the community.
"However, there is a small minority who do not respect others and cause anti-social behaviour at the park, and we will continue to focus patrols at the recreation ground for as long as it takes."