The case of two men charged with revealing that the Australian Government bugged the highest levels of the East Timorese Government was heard in court for the first time in Canberra on Wednesday, amid calls for the charges to be dropped.

Neither former spy 'Witness K' or his co-accused, lawyer and former ACT attorney-general Bernard Collaery, were present in the ACT Magistrates Court for the afternoon hearing, however dozens of protesters called on the Federal Government to drop the case against the pair at a rally outside.

The pair were charged earlier this year with conspiring to reveal secret information relating to an incident where Australian Government agents bugged the cabinet room of East Timor during negotiations between the countries on oil and gas.

Witness K and Mr Collaery were charged with conspiring to share information covered by section 39 of the Intelligence Services Act, which covers secrecy and the unauthorised communication of information.

The charges could see each man spend up to two years in jail.

Much of the case is shrouded in secrecy, and it is illegal to reveal details of the spying operation or reveal Witness K's identity.

Independent Tasmanian MP Andrew Wilkie joined protesters in calling for the charges to be dropped. ( ABC News: Ian Cutmore )

It is understood Mr Collaery has been served with a national security order which prevents him from discussing the case or court proceedings.

The court was on Wednesday open to the public, however the Federal Attorney-General is expected to request that much of the evidence be heard in secret.

The proceedings focused on how national security information could be handled as the case proceeded through the courts, and both parties said they would attempt to reach agreement on the matter before the charges are next heard in October.

Outside court on Wednesday morning, protesters including independent and minor party MPs Andrew Wilkie, Nick McKim and Rebekah Sharkie demanded the charges be dropped.

"It is outrageous that we are doing this, that our government is doing this in our name and not looking deeply at who in the previous Howard government was involved in the spying," Ms Sharkie said.

Mr Wilkie said he had faith the men would be cleared by the court.

"Let's just hope now that the justice system in the ACT gives these two men a fair hearing and comes up with the outcome that we would all hope for," he said.