One, involving a mobile home and a caravan, is on a roadway outside a graveyard in Fermoy and the other is located in a county council-owned picnic area.
Cork County Council officials said legal action would be taken very shortly to remove the Travellers under the two sets of legislation.
They made their comments after some councillors expressed concern no actions were being taken to remove the mobile accommodation, especially from outside New Kilcrumper Graveyard.
A mobile home and a caravan have been parked outside the cemetery by a Traveller family, following a circuit court order obtained by the county council which forced their removal from the nearby Beechfield housing estate. The family had been offered emergency accommodation but chose to relocate to the cemetery, on the north side of the town.
Council officials said that as the mobile home and caravan were parked on a public road outside, the action amounted to a breach of the Road Traffic Act, being an obstruction.
In relation to the mobile home parked at the picnic area on the south side of the town, they said that powers of the Housing Act would be used to remove a family there.
Council officials said they had “issued instructions” to the gardaí to act on both of these powers.
They made their comments at a meeting of the Charleville-Fermoy municipal district council after Cllr Noel McCarthy asked what steps were being taken to remove both encampments.
He said it was “unacceptable” that the encampment should be allowed to locate outside a graveyard.