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Legal action is being taken after travellers moved onto a field in Twydall.
A group moved onto the recreation ground off Cornwallis Avenue, near McDonald's, last Wednesday, and Medway Council says proceedings have begun to move the group.
Twydall Cllr Mark Prenter (Labour and Co-operative), said it was important to remember the rights of both residents and travellers.
"They've just moved in and we've been in contact with council officers, who will be moving through the normal procedure to have the removed.
"There's a legal process because they have their rights of course."
"I've had a look at the site - and they're keeping themselves to themselves. Obviously we have to think of the residents because it's an intrusion on their lives possibly, but not all travellers are bad. Lots just want to settle for a while and then move on."
A statement from Medway council said: "We are aware of the travellers in Cornwallis Avenue and we are following a civil legal process to move the group on as quickly as possible."
Around 20 vehicles are parked up on the site.