Mediation proceedings begin today in the court challenge over the nomination of Muckaty station as the proposed site for a nuclear waste dump.

Traditional Owners have reaffirmed their opposition to the facility claiming that the government failed to consult all traditional owner groups.

This comes after legislation enabling the facility to be built at Muckaty, passed through the House of Representatives on Tuesday.

Dianne Stokes Nampin, a traditional landowner of Muckaty station says that the consultation wasn't with the correct owners. 

"Every Traditional Owner knew about the waste dump coming to our land. Everyone knew that it was going to happen. 

"Everyone knew that the wrong people gave permission to have that land destroyed by these government people who weren't listening to the main Traditional Owners.

"They should have, at least, come and sat with us and talked with us."

Member for Lingiari Warren Snowden spoke earlier this week on ABC Radio in Darwin.

"They (Traditional Owners) can dispute the Northern Land Council's decision making process...that is their right.

"I am not going to comment on the merits or otherwise of the case but if the court comes down on their side, then the Commonwealth will respect the decision."