They are due to appear at Derry Magistrates’ Court this morning for a first remand hearing.
A 50-year-old man is also to face the same court for encouraging or assisting in rioting.
This relates to an incident at Rossville Street in May this year.
Police say that more arrests will follow after evidence is gathered by its Public Order Enquiry Team which is sifting through CCTV footage.
Part of the focus will be on trying to identify the gunman who fired six shots at police in the city last night.
Chief Inspector Neil Beck said: “For a fourth consecutive night police officers dealt with violence and disorder. #
“Around sixteen petrol bombs and five paint bombs were thrown from the Bogside area towards the city walls and at police.
“This can only be described as a blatant bid to murder police officers, shots were fired at police close to our city’s walls.
“We believe that around six shots were fired striking the walls and nearby trees, however fortunately none of our officers were injured.
“Police officers should not be targeted under any circumstances and their lives should not be put in danger by simply doing their jobs, attempting to keep people safe.
“I am appealing to those with influence in the area to please assist us in trying to bring this unnecessary and unwanted violence to an end. This isn’t wanted by the community and those involved are urged to cease this activity immediately.
“A number of males have been charged in connection with disorder over previous evenings and two of those are due to appear in court this morning. We have a robust strategy in place to identify those involved in the trouble of recent days and I am confident of further arrests. Anyone with information is asked to contact us on 101.
“Alternatively, information can also be provided to the Crimestoppers charity on 0800 555 111, which is 100% anonymous,” added Chief Inspector Beck.
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