WAM news agency said the hearing at the state security court in Abu Dhabi was devoted to procedural measures, including the appointment of lawyers.
The judge then adjourned the trial to September 28.
Earlier this month, the prosecutor general accused the defendants, who include both Emiratis and foreigners, of plotting attacks aimed at trying to "seize power and establish a caliphate".
He also accused them of creating a group "with a terrorist, takfiri (Sunni Muslim extremist) ideology".
The Islamic State group, which has set up a "caliphate" on territory it has captured in Syria and Iraq, follows the takfiri ideology, as does Al-Qaeda.
It was not immediately clear if the 41 suspects were accused of links to either group.
However, the prosecutor has said they were in touch with "foreign terrorist organisations... To help them achieve their goal".
The defendants could face the death penalty if found guilty.
They are also accused of setting up cells to train members in handling weapons and explosives in preparation for attacks in the UAE.
Such mass trials on terrorism charges are rare in the UAE which has largely been spared the Islamic militancy that has hit other Arab states.
The UAE is part of a US-led coalition that has been carrying out air strikes against IS in Syria since September last year.
The wealthy Gulf state has upped security measures in the aftermath of the 2011 Arab Spring uprisings.
In July, it adopted tougher anti-terror legislation and introduced the death penalty for crimes linked to religious hatred and "takfiri groups".
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