A Federal Court judge has ruled that traditional owners of a bay in north-east Arnhem Land in the Northern Territory have native title rights to the land in that region.

Two related cases in regards to the Blue Mud Bay claim were heard in the Federal Court of Australia.

In the first case, Justice Brad Selway said the applicants had native title rights to the land and sea between the low and high water mark.

The area is already considered Aboriginal land under the 1976 Aboriginal Land Rights Act.

The second case was a challenge to the power of the Northern Territory Government to issue commercial fishing licenses in the region.

Justice Selway said it was inappropriate to make any declarations in this case in regards to the Government's powers.