At around 2.15am, firefighters from Rivelin station were called out to a skip blaze in Crimicar Lane, Fulwood.
The cause of the fire is not yet known.
Doncaster firefighters were sent to a bin fire in Cooper Street, Hyde Park at around 2.30am.
One appliance was sent to extinguish the blaze, the cause of which is not yet known.
Firefighters from Lowedges station were called out to rubbish, which included aerosols, that had been fly-tipped and then set alight in woodlands off Houndkirk Road at around 6am.
A spokesman for South Yorkshire Fire and Rescue said the fire is believed to have been started deliberately.