The disturbances have occurred in unionist areas on the Waterside of Derry.
Petrol bombs and masonry were thrown at officers during disturbances in the predominantly unionist Rossdowney Road/Lincoln Court area of Derry on Thursday.
Earlier in the week, similar scenes were witnessed in the unionist Tullyvalley area in the Waterside.
Shortly after 9pm on Thursday, youths with petrol bombs and masonry gathered in the Rossdowney Road/Lincoln Court area and placed pallets on the road before setting them alight.
A digger parked nearby was also set alight.
The PSNI said its officers came under sustained attack when they responded.
Firefighters who attended the scene were also attacked.
PSNI Derry City and Strabane District Commander, Chief Superintendent Darrin Jones, said: “It is extremely disappointing that for four consecutive nights we have witnessed scenes of anti-social and criminal behaviour in the Waterside.
“These reckless attacks are not wanted by anyone and do nothing but cause harm and damage to the local community who we know just want to live in peace.
“I will again stress young people engaging in this type of criminal behaviour are risking not only their own safety, but they also face the possibility of a criminal conviction which can have life-changing consequences.
“We are appreciative of the efforts of those in helping to de-escalate the disorder this week.
“Our investigation continues, and I am appealing to parents and guardians, and all those who have influence, to help bring an end to the wanton destruction that we have seen in the Waterside this week.
“There is absolutely no justification for it and it has to stop.”