Paul McIntyre, 51, and Christopher Gillen, 38, both charged with riot and petrol bomb offences, were refused bail at Londonderry's magistrates' court.
They were arrested on Thursday. They refused to stand and recognise the court on Saturday.
McIntyre is also charged with the arson of a hijacked vehicle while Gillen is also charged with the arson and hijacking of a tipper truck.
The prosecution alleges that both men are connected to the New IRA (Irish Republican Army) paramilitary group, which orchestrated the rioting on April 18 and has since claimed responsibility for the death of journalist Lyra McKee.
The 29-year-old was shot in the head.
A police detective told the court that footage from security cameras and mobile phones showed two masked men in identical clothing to the defendants leaving the hijacked tipper truck, carrying a crate of petrol bombs and deploying them at police officers.
"Police believe these were the ring leaders, that's obvious from footage," the detective said.
"I have to bear in mind these gentlemen, there's no evidence either of them belong to any paramilitary organisation but they are a part of an organisation with a defined ideology."
On the possibility of them being released from custody, he said: "There is no address anywhere in this city which would be suitable in this case, at any stage. I will refuse bail."
The killing of McKee led to calls for politicians in Northern Ireland to agree to restore the province's power-sharing institutions.
A breakdown of trust brought down the Northern Irish Assembly in January 2017.
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