One of Australia's longest-running Aboriginal land rights claim is facing another hurdle with no-one at the helm of an investigation into a $32 million pollution problem on the site and clean-up due to begin this month.

A federal parliamentary committee into pollution on Commonwealth Government land near Darwin was due to hold public hearings in the Northern Territory later this month.

But these hearings could now be put behind schedule.

The hold-up represents another blow to the Kenbi land claim, which was lodged 36 years ago in 1979 and has still not been fully resolved.

Months after the chairwoman of the committee's inquiry into the proposed $32 million remediation of the site resigned, a replacement member has not been elected.

A member of the committee told the ABC he was "not sure" why this had not yet happened.

Graham Perrett, the committee's acting chairman and a federal Labor MP, said it was an "unusual situation" that the committee was still without a chair while the inquiry into the remediation project was supposed to be getting under way, and with the project itself due to begin this month.

Cox Peninsula Land Claim: The Kenbi land claim was lodged in 1979 and is Australia's oldest unresolved Aboriginal land rights claim.

The Kenbi land claim was lodged in 1979 and is Australia's oldest unresolved Aboriginal land rights claim. A Federal Government report highlighted the risk posed by asbestos and other chemicals to local bore water on land subject to the claim.

A Federal Government report highlighted the risk posed by asbestos and other chemicals to local bore water on land subject to the claim. The Government wants to spend $32 million to clean up the land and says this will be the final step before handing the land over to Indigenous traditional owners.

The Government wants to spend $32 million to clean up the land and says this will be the final step before handing the land over to Indigenous traditional owners. The Northern Land Council, which helps Aboriginal people manage traditional lands, says remediation works shouldn't hold up the claim, and land should be given back immediately.

Mr Perrett said he did not know why a new member and chair had not yet been elected.

"We had a meeting last week. I'm not sure why a new member wasn't elected then," he said.

The last regular meeting of the committee was on February 12.

A spokeswoman from the Public Works Committee Secretariat told the ABC it was typically up to the Government to appoint a replacement member for the committee.

In most cases, the committee would then choose one of their number to be the chairperson.

The spokeswoman said it was unlikely the inquiry into the pollution clean-up on the Kenbi land would go ahead without a chair.

She said no date had been set for the hearings due to take place in the Northern Territory, or for the start of the clean-up.

The Kenbi land claim covers the Cox Peninsula, west of Darwin, which had been used by the Commonwealth Government for over 70 years for communications and defence purposes during World War II, with a lighthouse and other government buildings spread over 4,750 hectares of land.

An old radio facility, pictured in 1966, situated in Section 34 of Cox Peninsula. ( Supplied )

In December, a report by the federal Department of Finance found government buildings on the peninsula were harbouring dangerous levels of asbestos, pesticides, heavy metals and other pollutants.

It said these "pose a significant risk to human health" and represent a "liability for the Commonwealth".

In December, following the recent federal report, the federal Parliamentary Public Works Committee announced it would conduct an inquiry into the proposed $31.8 million remediation of the site.

But that same month the head of the committee, Karen Andrews, was promoted to the federal Cabinet and had to resign from her position on the committee.

The proposed clean-up of the area is also due to begin later this month.

There have been longstanding concerns about pollution in the area, including a 2010 clean-up project that was aborted after it ran over time and over budget.