Lord Justices Neill, Leggatt and Millett are being asked to rule on the definition of 'gypsy' within the meaning of the 1968 Caravan Sites Act, in an appeal against decisions by South Hams DC, Dorset CC and Glos. CC to evict four travellers.
The travellers insist that as 'persons of nomadic habit of life' they come within that definition, and that they have special rights under the Act which obliges CCs to find adequate numbers of camp sites for gypsies 'resorting to or residing in their areas'.
But the local authorities insist that the statutory definition of 'gypsy' means more than simply travelling from place to place.
The three-judge Appeal Court did not indicate when it would deliver its ruling on the case.