An appeal hearing for five men convicted of conspiring to commit an act of terrorism has started under tight security at the NSW Supreme Court.

About a dozen police officers and the dog squad were at the court and the media were kept behind black and yellow tape for the hearing, which was adjourned after less than an hour.

Mohamed Ali Elomar, Khaled Cheikho, his nephew Moustafa Cheikho, Abdul Rakib Hasan and Mohammed Omar Jamal were jailed for maximum terms of between 23 and 28 years in 2010.

The men, who were found guilty of conspiring to commit an act or acts in preparation for a terrorist act between July 2004 and November 2005, are appealing their convictions.

The plot included stockpiling firearms, ammunition, chemicals and laboratory equipment.

The men also had recipes for making explosives, as well as other instructional material including the "Sniper Handbook".

During Monday's brief hearing, Chief Justice Tom Bathurst said there was no summary of the trial available and they were in effect "starting from scratch".

In order for the appeal hearing to run smoothly, he asked that a summary and additional material be provided.

The matter was adjourned until Tuesday.

It is understood the men will be appealing their convictions on a number of grounds, some of which will be shared.

Khaled Cheiko's barrister, Gregory James QC, said the verdict regarding his client was unsatisfactory and the combination of events raised at the trial "do not amount to a circumstantial case".

In sentencing the five men in 2010, Justice Anthony Whealy said they had a "vast quantity of extremist or fundamentalist material" including images glorifying the 9/11 hijackers and images of "heroes of the jihadist movement".

He also said the evidence did not establish that any firm conclusion had been reached by the conspirators about the nature of the action or its target.