The separate groups have been staying at Stamford Road in Weldon and land off the A6 in Burton Latimer.
But Northamptonshire County Council was due to attend Northampton Magistrates’ Court on Friday to ask JPs to grant civil orders under Section 77 of the criminal justice act.
The land at Weldon is owned by Corby Borough Council.
People living in nearby East Crescent has reported issues with anti-social behaviour to police in recent weeks.
The land off the A6 at Burton Latimer is owned by the county council.
Section 77 of the criminal justice and public order act 1994 can be used by a local authority to remove travellers from any land in their authority, irrespective of ownership.
An order allows council officers to enforce possession or to use private bailiffs to do so.
The travellers are then not allowed to return to the same location inside three months. If they return, it is a criminal offence.