A team of lawyers led by barrister John Purnell, SC, represented ANU against the cafe owner's Kamy Saeedi Lawyers' partner David Robens in a joint hearing of two cases each party brought against the other in the ACT Magistrates Court on Monday.

The ANU and Mint International Pty Ltd, trading as The Gods Cafe and Bar, had lodged competing cases against the other party after the university ordered the cafe owner, Jaye Min to vacate the premises earlier this year.

The cafe was one of several leaseholders in a university-owned building Mr Purnell said was slated for demolition in 2014 as part of the multi-million dollar Union Court redevelopment.

Mr Min's lawyers had lodged the first case, challenging ANU's contractual ability to evict the cafe with less than six months notice, before the ANU's counter-claim that that application to court was lodged after the statutory timeframe allowed.

Mr Robens argued the university had to give six months notice, given his client's lease was until 2018 with an option to extend to 2023, rather than the April notice given to vacate by July.

But Mr Purnell argued the university had given Mr Min appropriate notice and that he had known of the planned demolition, which had been touted before he signed the lease.

Mr Robens also said he had been given little notice to complete preparing for a hearing after it was lodged last Friday, arguing for a fortnight to prepare.

Mr Purnell said that he understood on the current schedule, if all the premises were not vacated by July 3, the university could face an initial charge of $1.1 million in costs and about $80,000 for each day the works were delayed.

But neither party could provide the court with a copy of, or the original, contract for Mr Min's lease of the cafe premises from the university.

A further hearing of the case was expected before the end of June.