The police said they dealt with a number of anti-social behaviour incidents in the Madam’s Bank Road area of the city on Saturday and Sunday.
Road barriers were pulled out onto Madam’s Bank Road and set on fire. Traffic lights were also set alight.
There were no injuries reported to the police.
The fire service had to withdraw from the area on Sunday night after stones were thrown by young people.
Police also came under attack from youths throwing bottles and bricks. A petrol bomb was thrown, but failed to ignite.
Chief Inspector Jonathan Hunter said: “This weekend we have again seen youths take to the streets of Derry causing damage and misery to the local community and businesses.
“I cannot understand what these youths hope to achieve.
“No-one wants this.
“Everyone should be in a position to go about their daily lives and come into the city without worrying about this mindless criminal behaviour.
“It has to stop.”
He also urged parents and guardians to “please help prevent young people from becoming involved, or caught up in these activities”.
“Not only are you putting yourself in danger by becoming involved in activity such as this, you will also face consequences that can be far reaching and can seriously impact on your future opportunities for work, travel and being accepted for university,” added Chief Inspector Hunter.