The first petrol bomb was thrown at the Fountain estate, hitting a house.
When police attended the scene, a second petrol bomb was thrown at their Land Rover, breaking a small back window.
On Tuesday night, a petrol bomb was thrown at police in the Lecky Road area at about 10.20 pm.
About two hours later, a number of youths gathered in the area of Fahan Street and threw stones and a number of petrol bombs at police, damaging the windscreen of a police vehicle.
Petrol bombs were also thrown over the city’s walls.
PSNI Derry and Strabane District Commander, Chief Supt Emma Bond has called on those behind the violence to stop immediately.
“It is disappointing to see this type of disorder in our city,” said Chief Supt Bond..
“We understand the impact this type of anti-social and criminal activity has on residents in the area who have a right to live in peace and enjoy their homes.”
She added: “I want to appeal to parents to know where their children are, who they are with and what they are doing.“I would also urge those in the community to continue to use their influence to help prevent a repeat of this activity.
“And my appeal to anyone who has been involved, or anyone who is tempted to become engaged in this behaviour, to stop and consider the consequences of their actions, and desist immediately.”
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