The order included the Stough Nature Center, the Burbank Police Department said.
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There were no immediate reports of injuries in the so-called Wildwood Fire, which broke out shortly before 4 p.m. near the police department's firing range and training facility and spread to the hills above Sunset Canyon Drive.
At least eight Burbank Fire Department units contained the blaze by 6:30 p.m. with assistance from the Los Angeles County Fire Department.
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All roads in the evacuation area except Wildwood Canyon Road are expected to remain closed overnight, police said.
The cause of the fire was unknown.