Cellist David Pereira and violinist Tor Fromyhr applied to have their fixed-term contracts converted to permanent employment under a clause in the university's new enterprise agreement.

Both were denied conversion to ongoing employment and were not offered further contracts.

They have raised disputes with the university through the National Tertiary Education Union.

Pereira was told in an email that it was "now a time to allow a new generation of talented musicians and academics to establish themselves and be well-positioned to lead and shape the ANU School of Music into the future".

Pereira said he believed the stress involved in his uncertain employment situation contributed to the heart attack he had in January.

"It's a very challenging, somewhat unhealthy and toxic workplace when you get a succession of short-term contracts from year to year," he said.

"You wonder whether you're going to have employment next year ... it's quite a hard life."

Fromyhr, who has an Indigenous background, has been involved in Dr Chris Sainsbury's initiative supporting young Indigenous composers.

"There are probably, I think, four current Indigenous musicians within the tertiary environment in the classical sphere in this country. If my job is finished, there are three," he said.

"There are students that have come, a large number, that have come here specifically because we encourage them to come."

A university spokesman said the ANU did not comment on individual staffing matters.

"The university is committed to giving more staff on fixed-term contracts greater job certainty where those opportunities are available," the spokesman said.

"All transfers and reviews of possible transfers are undertaken in accordance with the university's enterprise agreement and relevant workplace law."

National Tertiary Education Union division secretary Dr Lachlan Clohesy said the Fair Work Commission may need to settle the dispute if they couldn't reach a satisfactory conclusion.

"These staff should never have been employed on an insecure fixed-term basis in the first place. They are entitled to continuing employment, and we're standing up for and with union members to achieve secure work," he said.

"The shabby treatment these long-term ANU staff have been subjected to has been shameful."

Cello and violin students were shocked when they found out their lecturers could be leaving the university.

"I'm about to finish my last performance course and I've had Tor with me through the entire three years of my degree," music and science student and cello player Anika Chan said.

"To have him suddenly ripped away at probably the most important assessment that I'll have in my music degree was just shocking."

Enola Jefferis said she decided to move from regional Victoria to study at the ANU specifically to learn from Pereira.

"David gave me a call after seeing my application and just really said he would be able to support me and really support my growth in music," she said.

"And that's something that's really, really important for music, that you have a much closer relationship with a teacher than you do in many other degrees."

Fromyhr has been working at the ANU for 27 years while Pereira was first a senior lecturer in cello in 1991.

They had their permanent roles cut during the controversial budget cuts and restructure of the School of Music in 2012.

After a period where students were given money to have private tuition, both were brought back on fixed-term contracts that have been extended since 2017.

Fromyhr's contract was extended one year to March 20, 2024 while Pereira's contract was extended until February 9, 2024, with the understanding the school was waiting for a review to be completed.

The university is only meant to employ staff on fixed-term contracts if they are doing a specific task or project with a start and expected end date, or if the role is attached to external funding.

Under the new enterprise agreement, employees on existing fixed-term contracts who were employed against these rules are entitled to a continuing position.

The two musicians said the nature of their work was ongoing, rather than as part of a specific task or project.

"The main point is we were doing excellent work that still needs to be done. And we've been replaced without explanation, except it's time for a new generation," Pereira said.