Easter Rising parades: Police investigate marches in Lurgan, Coalisland and Ardoyne
Police are investigating three parades commemorating the 1916 Easter Rising in Lurgan, County Armagh; Coalisland, County Tyrone and Ardoyne in Belfast.
Unionists complained after masked men paraded through Lurgan on Saturday and marchers wore paramilitary-style uniform in Coalisland on Sunday.
Officers are examining "suspected breaches of Parades Commission determinations in Coalisland".
They are investigating "un-notified processions in Ardoyne and Lurgan".
During the Lurgan parade, masked republicans marched from the Kilwilkie estate to St Colman's Cemetery in the town.
Police said they were not notified of the event.
Democratic Unionist Party (DUP) councillor Carla Lockhart said it was "deeply concerning".
"It is certainly very worrying, we are in a new Northern Ireland, this is unacceptable behaviour and I have been in contact with the PSNI who will be investigating this incident," she said.
"It is very worrying to see masked men walking through the streets of Lurgan."
The TUV's Roy Ferguson said the parade was a "totally unacceptable state of affairs" and he would be "contacting the PSNI to demand an explanation as to why the terrorist show of strength was permitted to take place and how they propose to bring those involved before the courts".
On Sunday about 50 people in paramilitary-style uniforms led a parade associated with dissident republicans in Coalisland.
In a statement, ACC Stephen Martin said: "In policing all events over the Easter weekend our overriding desire is to ensure that commemorative occasions, parades and protests pass off lawfully and peacefully.
"Our focus is on keeping communities safe and our job, with a few notable exceptions, has been made that much easier because of the responsible attitude of all parties concerned.
"We are however, investigating suspected breaches of Parades Commission determinations in Coalisland and un-notified processions in Ardoyne and Lurgan. We have gathered evidence at these events and will present reports to the Public Prosecution Service with a view to holding individuals accountable."