There have been a number of protests over the decision to remove the union flag from its permanent position at Belfast City Hall.
About 20 loyalists carrying union flags, were allowed to walk through the centre of Londonderry after a stand-off with the police.
Police have said they will send a file to the Public Prosecutions Service about the actions of some protesters.
In Belfast, a protest closed the bottom of the Shankill Road for a time.
Since Friday night 19 people have been charged in connection with violence at loyalist protests.
On Saturday, up to 2,000 people at Belfast City Hall held a peaceful protest.
However, violence broke out in some parts of the city afterwards.
A police officer injured during trouble has been discharged from hospital.
There was criticism of the timing and location of Saturday's rally on one of the year's busiest shopping days.
The police have said paramilitaries have organised some of the violence.
Loyalists opposed to new restrictions on flying the union flag at Belfast city hall have been holding protests across Northern Ireland all week after the city council voted to fly the flag on about 20 designated days.
Nationalists at Belfast City Council had wanted the union flag taken down altogether, but in the end voted on a compromise from the Alliance party that it would fly on designated days.
Unionists have said they consider the changes regarding the union flag to be an attack on their cultural identity and there have been protests in different parts of Northern Ireland since it was taken.